The San Francisco 49ers versus the Kansas City Chiefs. Who? That's really what we're getting here in a few days, boys. Now, obviously, I'm a Butthurt Lions fan, and many of us probably wanted to see the Ravens go on. But at the end of the day, it's still the Super Bowl, right? And if I can put my hating ways aside, I honestly think it's gonna be a great game no matter what. Because, look, either Mr. Irrelevant, the lowest paid quarterback in the NFL, the 22-year-old Brock Purdy, is gonna have a Super Bowl ring before most of our poverty franchises. Yeah. Or Patrick Mahomes will actually be on track to be a better player than Tom Brady. I know you hated hearing that. I know just how bad that bothered you. But if Mahomes gets this Super Bowl and can maintain this pace, he just might go down as better than Brady. My point is we basically jumped from Michael Jordan to LeBron James with no gap in between. They literally, like, Tom Brady started to exit the league, and Mahomes started to take it over. Maybe the scriptwriters knew what they were doing all along. Which is not something I can say for the Wheel of Mutts scriptwriters. Or maybe I can, because our current record is three and two. Three losses, and we're booted. We restart the season. Five wins, and we make the playoffs, which means we are two games away from a shot at a title. Now, there were some big changes last episode. I want to go over them.  Two pick sixes in the first half. And that landed us a plus one at one position. So we took Drew Brees. We yaded him out of the lineup. And we added 95 overall-limited CJ Stroud. He's boosted to a 96. His stats are obviously incredible. He gets an incredible ability stack. And we saved two AP on Drew Brees, which freed up mid and elite on Zay Flowers and identifier on John Runyon. Really excited about identifier. I'll be able to see my opponent's user now, which I haven't done the entire season of that in 24. We also added 93 corner Devon Hester. We added Malik Hooker, who we put at strong safety. And my backup strong safety should not be DeMonte KZ. It should be our prestige, Derwin James. Got to say, Derwin James is his first time truly getting bench, but he will come in on nickel formations. And honestly, he's been great. This might be one of the best 90 overalls I've ever used. Now, we still have some holes in this lineup, though we're a 90 overall, but we have a silver middle linebacker. We've got a mediocre D tackle to and left end. Prime time is a little outdated. Isaiah Oliver is obviously outdated.  And Fred Taylor, obviously not the guy you want to fullback. Jake Ferguson, not the guy you want to back up tight. You know the rules, gentlemen. The next Wheel of Mott episode after this is actually going to be on the day of the Super Bowl. So we might make the playoffs on the day of the Super Bowl. That would be a pretty cool way to kick off Super Bowl Sunday. All right, boys. Let's get into our first wheel spin in this episode. A lot of holes to fill. I'd like to build the O-line for sure. And I'm not going to get that choice, but I am going to get an insane player. It's playoff wheel defense. So these are all the teams that made the playoffs this season in the NFL. We can take one of our choice, defensive player. It's not Temple Bay. It's the Fratidelfia Eagles. You know what's funny about the Eagles is I already have one of their very good defensive players. And that's Jalen Carter. He's actually a prestige. The 94 overall for the Philadelphia Eagles is big play Slay, a former Detroit lion. This is an incredible option for this team. I was talking about how prime is a little bit outdated.  And he probably gets a really good discounted ability. So very good option here in Darius Slay. Most likely it's Darius Slay. We could take Nolan Smith. Doesn't make a whole lot of sense for this team. I guess he could be the backup middle linebacker. You could take Carmichael. Carmichael does make a lot of sense, but this dude is the most meta card in the game. I see too much of Harold Carmichael. We're gonna break them all. I'm going Darius Slay. 400,000 coins for Darius Slay. I'm always happy to get a former lion. So I'm gonna put Darius Slay at CB3. Although I do need to see what ability he gets. If he gets a discounted knockout, I might have to put him at CB2. Deep out zone KO for two. Do we try this? I wanna try it. I haven't used deep out zone KO yet. And I've been talking about trying to get that on this team. So let's go for it. I'll go universal coverage. All right, thank you Philadelphia Eagles. All right y'all, the second wheel spin offensive line MLB2 defensive line. That's what we're looking to upgrade right here. It's not gonna be jackpot. Honestly, this is one of my favorite ones. This is such a fun one to get. I'm playing as the Cleveland Browns. We're taking on the New York Jets. We've got to Sean Watson. We've got Nick Chubb. We get 5,000 coins to spend on one player for every round that we can complete. We'll start with the flood concept. You just gotta complete a pass. Keep it simple. Power run, Nick Chubb. Find it buddy. Find it. I got in there. Simple read, level three. First down secured. Stay in the hotspot. This could not be easier. Oklahoma defense. Prevent a first down. Easy read. Extra life challenge. Just gotta get to the hotspot. We've definitely got the numbers. Should be too easy, right? No, don't get, that was embarrassing. Although we don't lose a life since that was an extra life challenge. No lives lost, about to be level 10. Oh wait, I'm the blocker. I'm blocking. I thought I was Nick Chubb. All right, I gotta let these idiots make the tackles. How would this CPU ever get in the end zone?  Good. He's walking himself out of bounds. How am I supposed to prevent him from doing that?  Please. Please, what are you doing? How would you ever score this?  Okay. 45,000 coins to spend on one player. Just gonna pick up the most usable offensive lineman. Can't quite get to a 90 overall. Gonna pick up 89 overall Cam Juergens here. He's actually a really fast guard. 78 speed, 80 excel. So from running any slip screens or anything like that, he'll be pretty good. He's just under our budget. We got nine rounds times 5K, 45,000 coins. Not what I was going for. And in my defense, my current right guard's a 79 overall. So this is a plus 10 and it takes us to our third and final wheel spin. I'm really sure what I wanna do with it at this point. I guess we made an O line upgrade. We'll find out it is a sole hacka punch. So we can take one player on this team and take them to their best possible version. Willie Rove definitely has a much better card than 86 overall, though. I don't know what his best card is. Let me look it up. So initial option, Willie Rove has an 89 overall. Fred Taylor has an 87, I guess. We could boost our fullback a little bit. Does Jake Ferguson have anything? Jake Ferguson does have a 90 overall harvest tight end. So that would be a plus 10. Our backup tight end would get a lot better. That's a pretty good option. You know who's got an insane card that was Aaron Donald? He's got that Terminator. I think I'm going Jake Ferguson. I definitely like a better backup tight end. That 80 Jake Ferguson is not worth a thing right now. So 90 overall harvest tight end. Jake Ferguson, obviously a huge step up from what's in there right now. It'll be a halfway decent threat to throw to as a backup tight end. I do have a lot of sets with two tight ends. I talk about that a lot. So Gronk's not the only guy who's gonna be getting thrown to. I don't think the upgrade on Willie Rove was big enough and I don't think Aaron Donald would have been impactful enough. All right, Jake Ferguson is in. Cam Jurgens is in. And of course, big play Slay is in. Adorea players added his team. We still got no MLB two, D-Tackle two left end. And left tackle center definitely needs some help. But we are three and two. This is a must win scenario. Let's see what the challenge wheel has got for us. Come on baby. Last challenge wheel was four passing touchdowns. We didn't have time to come. Have I ever done this one successfully like for real? I know I've gotten really close. 55 plus fantasy points with one player. PPR scoring, of course. Somebody's gotta have a monster game if we're gonna complete this. Pop three, of course. It's Stroud, Zay, and most of three playoff limits. He's got the Derek Carr. Oh my God.  And now I've gotta play him in my very next game. It's a night game, five minute quarters. Zay Flowers does have this RPO here and he, look at identifier already. He has usering stray hand. Now on Ray Lewis. He can't get to Zay Flowers. We're gonna take the quick RPO. Good blocks. Zay Flowers? Damn, it is weird having identifier but I really like it. Let's take a look. I'm gonna take Zay Flowers. Getting to 55 plus is gonna require me to force feed somebody. He's gonna leave Zay Flowers once again. I'm sorry to be spamming. He's leaving it and Zay Flowers already has 5.5 fantasy points. 25 yards, three receptions. Sit in the pocket. Clean, clean, Zay Flowers. Yup. That's exactly what is exactly what I wanted to happen. Okay. Zay Flowers, post.  He's on Jedevian Clowny this time. Let's go weak side. We're gonna go to Flowers side. Great blocks. Excellent. That's excellent work. Shit. He almost sacked me but he doesn't get it. I don't know how he got through the middle untouched right there but we survived. I don't wanna think about Zay Flowers too much. I feel like I just gotta put this ball in the end zone, right? Grand Kitch, it's gonna be a tough catch. That was basically what a center does to a point guard in the post. He boxed out Pat Tillman.  This is a huge play right there. 3rd and 5, huge conversion.  I'm handing this off to Dree Archer. Sorry, Zay Flowers. I know we got challenges to complete. They didn't get it. 2nd and goal. Let's go. Jet sweeps, Zay Flowers. He's got it.   Okay. 3rd and goal. Big play. Excellent blocking right there. Zay Flowers is gonna clear. Monster drive. Runk and Zay Flowers made two and... Look at this, dude.  Let's see if we can cap this off. He's only got a three man rush. He's still on Vince Willfork. I'm going to Dree Archer. That is greedy. I threw that too quick. 1st and 10, and I just went... Punch out. Oh my God. I whiffed the avalanche and then I got the punch out and then he recovered the fumble. Damn. I tell you what, boys. One of the biggest changes I've made this year that has helped my game so much.  You get so many knockouts and I'm not quite sure who just got that knockout there but that's an avalanche. And that is two fumbles that he's recovered. Damn it. Who is this over here? It was Devin Hester. Devin Hester just got that knockout, dude.  Oh my God. It's so good. Yeah, whoopsies. But the best time to do it is when you've got extra bodies to make the tackle. 1st and 10. We have literally popped out two fumbles and we don't have the ball but you know what? This guy is dedicated to the run game. Maurice Jones, Drew, can't go anywhere. They're averaging a yard per carry. I expect a pass here. It's an RPO. I can get over here with Christian Harris. Huge play. 3rd and 4th. It is a pass. He's gonna check quick. Isaiah Lightly who catches it. 4th and 3th. He's no huddle. I expected that too. I think this is an RPO. I think it's an RPO. I gotta get to, oh, why is, who is Graham and why are you in? Who is Graham and why are you in? It's not an RPO. 83 is open.  Who is Graham and why are you in? Definitely could be a run. I gotta be ready with Ray Lewis and I'm gonna go on the lead cooker. It was an RPO and it's bottled by 85, Aaron Donald. No man in his right mind would run the ball after that pitiful ashram attempt. Yup, it's a pass. Oh no. Dude, honestly, we got two fumbles on that drive. We're gonna make him turn it over for real. Just hasn't happened quite yet. Got a block tree archer. Now he's on Vince Wilfork. I should be able to hit safe flowers underneath, we need to milk this clock aggressively. I haven't seen that glitch in a long time but Gronk did the thing on his slant where he decides to just dead stop in the middle of it. Hit him, take our PPR points and hopefully he's not trapped. Great blocking from Jamar Chase. Safe flowers the first down. The clock moves. We'll be at the two minute morning here soon. I don't think he can coverage Mark Chase on this. No, he can't. Dude, if he stays on Vince Wilfork he's gonna be in so much trouble because this RPO level will never not be open if he stays like that. I think I might be able to hit CD-Lam actually.  I don't know what got into me right there. I had it early, I threw it so late that tip-ups a little unlucky but that's totally on me, that was a horrible ball. All right, we just gotta get the ball back now. Let's win or go home. Aaron Donald, you gotta love this Aaron Donald man. Picked up nicely. Do we get the tackle we do? He's not gonna get the first, third and two. Just gonna check it down. Ooh, I was trying to go for the knockout there.  Let's let him get a lot more yards than he should have. Oh no, I'm on Aaron Donald's bed. He can go 80, he can go 80, he can go 80. Okay, he's just gonna take off with Derek Carr. He's gonna slide down third and three. I'm calling a timeout. Oh, I'm so close to that but I get the knockout. Let's go. Huge hit from Lewis fourth and three. I'll take the field goal. Honestly, we have an opportunity to potentially score right here too. Here's Gronk, great catch. Get down, five seconds on the clock. Can I get in field goal range and still get a time out of? Oh my God, that's a horrible ball. Honestly, it doesn't even matter that's a horrible ball. Yeah, he didn't have to be. I don't know why, but I just feel like we're gonna win this game. There she is. Beautiful defense, Lawrence Taylor. Dude, he's got negative five rushing yards.  Come on, boys. Trips tight end offset. Okay, so last time out of this, he blocked the running back. So I'm not gonna blitz really. Oh, I'm so unbelievably close to that. Let me have it. That's it or no, no. What?  That should have been intercepted by two people and he caught it.  He's picked up two fumbles. Oh, that's so frustrating. So run is an obvious run. Oh, it's an RPO action, stretch alert bubble. I don't know if I can get to this. Oh, I can. Huge tackle. Oh, wow, just unbelievably frustrating on that one. Could be a run play once again. Oh, it's the same play, stretch alert bubble. This is gonna be a tough. This is gonna be an uphill battle. Got a play strong. This is gonna be a CD-Lamp pass. This is a seam beater. He's in cover three. He will run the exact same thing. He will not adjust. CD-Lamp will catch it this time. And I still could have thrown that, but I can also throw this. Tree archer, nice check down, nice juke. Dude, he's actually gonna leave CD-Lamp again. This is just safer. This is so much safer. I'm not taking the CD-Lamp pass if I've got that. Maybe could have thrown that up. One gigantic stop. Tree archer, great angle route. Second and six. One, two, CD-Lamp will touch up. Does he got what it takes to close this game out on me? With really efficient clock management, he puts me in a serious hole. That's for sure. Patience, patience, patience, patience, patience. No, Jesus. Oh, I had somebody over there, didn't I? I had, I think it was Gronk wide open. And there it is. It's an RPO actually. It's an RPO. He's gonna accidentally keep it with car. He did not mean to do that. I'm gonna cook her and play a potential RPO here. Not an RPO. Great defense.  Third and 13, that was huge. I've been trying to get one turnover on this new dull game. Maybe I can get it here to dig. And there's a dig. Where are you shifting to? Where are you going, Lawrence Taylor? You're in the mid zone. This could be an RPO again. We just hand up. And we got the silver graham. The fact that he's like gone all the way down here, not shooting the clock, very good for us. Just gonna hand it off. That looked like it was second to nine. Same, my first rodeo champ. See what he comes out with here? He's gotta come out with a big pass, right? So if there was ever a time to intercept him, it's right now. He's gonna send that dig across, that late dig from 12. Going main coverage Blitz. Let's go!  Fourth to 12, that's okay. Hey, that switch up to the Blitz was ballsy, but it might have just paid off. He's gonna drill this. It'll be an eight point game. I can score and get a two point conversion.  Okay, so CD-Lam is open. I don't know what his obsession with this is, but he's open every time he does this. CD-Lam might be getting our challenge rule, but if I don't win, it doesn't matter. Archer's show! We'll go Jamar Chase on a whip. We're gonna switch it up just a little bit.  It's gonna owe for two right now on those. So he's gonna leave Dre Archer again under here. The juke inside's always gonna work. There's Dre Archer right in the middle. We got a ball game, gentlemen. There's Dre Archer, easy pass. 20 seconds left, we call a timeout. I've literally ran the exact same thing out of gun trips. I had this entire drive and last drive. The thing is, this same formation has an RPO. So I could whip the RPO now and he won't expect it. Or do I save this RPO for the two point conversion? I feel like if I keep it in my back pocket and he doesn't see it, it should be a free two point conversion, right? Should be, actually, yeah. I'm keeping this in my back pocket. I'm not using it here. There's Gronkh. Easy throw, great catch. I have one timeout left. I have 14 seconds. I have three shots at the end zone and I don't want to use RPO trap alert bubble because I want to use it for the two point and I want to stay in this exact formation so that he thinks it's the same play he's been seeing over and over and over. And I want to give this away. I think I can hit CD-Lam for the touchdown here and I think I got to go for it. Let's go. CD-Lam, touchdown! Now it all comes down to the two point conversion. I almost could run that exact same thing, couldn't I? I really could. It all comes down to this, 18 to 20. I think the RPO is there. He's on Vince Willford. It is, the RPO is there. We got to go. Throw the bubble, give me a block. What are you doing, Jamar? He got it, Jamar! 12 seconds, one timeout for the Steelers. We're almost to overtime, almost. He's got a timeout in eight seconds. He could really get in field goal range here. Straight up, 100% could get in field goal range. He calls it timeout. Oh my God, he has to hit a corner out now. He doesn't, oh my God, what? He doesn't even wanna risk throwing an interception? What? Oh my God, that's insane. I have never seen that. I guess it makes sense. I know it doesn't. I don't get that. He keeps his momentum or something? Fails, never. Fails, it fails. It fails right now.   And he gets the coin toss. Stretchyler bubble, stretchyler bubble. Every time.  Lawrence Taylor, you're all over that, man.   Third and one, huge play. Potentially a run, potentially some form of RPO. Throws it to that side, and he gets it. Nice play. He's gonna hand it off, not on Nick Bosa. Second and 13, huge defense. He is just spamming the RPOs. What? Ramsay, anime! It's, oh my God, it's right there. Ramsay had him locked up.  I'm playing that perfectly. I'm coming down at him, holding why I have lurk artist. Please let me have one.  I just got a defensive holding. Illegal contact, that's a brutal one right there. Definitely still could be a handoff. Then I got a amount of handoffs here. No, I'm a little shocked by this playbook.  We are jumping every ball. He just keeps catching it. What are we doing? I've been there every time on every ball. Goes Mojo, second and two. Game ain't over, ain't over til it's over. Corner out at 83. Stop it! You're throwing to the face of my players and nobody was hitting the ball. What are you doing?  Why deviate from the script right now when it's all going so well? We've got this gentlemen. Coach Suggestions, all carrier, conservative. Harrison Butker has every kicker ability. He gets a slow meter.  Gronk, once again. You don't want to guard it. I'll keep throwing it. 27 for 31, 283 yards. And the one interception is on me. CJ Stroud with an insane debut and the Vince Wilfwick user. Gonna go home with the loss here. Let's go three archer. It's simple. It's easy. Can't let him get a knockout on me right there, second and nine. Beautiful. Gotta remember every single time we can always switch to this RPO trap bubble here. And the issue is that it's Jermart Chase running it. When any time he presses, CDLAM is so open. One, two, CDLAM. Game! Ball game! I can take the field ball right now if I want it. It's a little too deep. It's a little bit. It's a little bit sketchy. I'm gonna take one more bubble out of Zay Flowers just to move myself a little bit closer. Only throwing this bubble if it is unbelievably open. I expect it to be. It is, hold those blocks, stay inside. Ball carrier conservative for that exact reason. 46 yard field goal for the game. Let's go! Two point. We got him both. We lose the coin toss. Red zone interception, marched down and ended the ball game. Oh my God, that might be. Oh! Honestly, I really don't know if we got our challenge wheel done. Unfortunately, he did quit. See, the thing is though CDLAM had two touchdowns, a ton of yards and receptions. I just feel like 55 plus is so hard. I feel like even if he had 15 receptions, 150 yards and two touchdowns, I feel like that's pretty realistic. He would have had 42 points. As a consolation, I'm gonna open a mystery pack. So rather than choosing a pack, I'll let fate decide if this is good or not the mystery pack.  So fate decided that I did not give 55 plus. Unless I get a linebacker, which fate is kind of looking out for me.  Yep, yep.  Basically. All right, boys, I love y'all. Thank you for watching as always. You just watched one of the best wheel and butts of the season. We move to four and two. So next game is really the biggest game. We win, we head to the playoffs. We lose, we're headed to Cancun to meet up with the Lions and the Baltimore Ravens. I love you boys. Thanks for watching as always. See you in the next one. Peace.


runs in four ribbies and after the game our Meredith Morocco, it's caught up with Judge and asked him about those two homers. I feel a touch of bad and, you know, I was happy to get those first three runs and kind of give us a lead, allow our pitching staff to go in there and do their thing. And I'm just happy to keep, give ourselves a lead. When we got a lead, this team is dangerous. You're a guy that's always taken a tremendous amount of pride in his defense. Just how difficult was that play to make there in the fourth inning?  And, you know, if I miss that, it could be a double triple or even inside the Parker.  You don't get to the plate for that first home run if Joey Gallo doesn't work the walk and then his home run the defensemaker there in the seventh inning. Nice to see him get going a little bit here in the second half. Oh, big time, big time. Joey's, you know, he's always works, works to count, works to good at bat.  Then later in the game, you know, against another tough pitcher, you know, hits a homer. Man, it just shows you what he's capable of.  This win almost overshadowed a little bit by the fact that Michael King walked off the mound there in that eighth inning. He's been such an integral part of the bullpen. What would it mean? What type of blow would it be if you guys lost him for an extended period of time?   Aaron, thank you. Thank you.


Jaws is back, baby. And this time, it's personal. Somehow. Someway. It's personal. As of recording, it's Shark Week. So I thought it would be appropriate to talk about a movie that's not only insulting to sharks, but also to film itself. Jaws, The Revenge, is the fourth and final installment to once again end on the sourest note possible. Let's fry this fish. Today's movie roast is produced by Colton Oakwist. He's been an awesome supporter of the channel, a great live stream moderator, my brother, and my friend. And believe it or not, YouTube can become a roast producer by heading over to patreon.com slash Adam Does Movies and signing up for the Mithril membership. Or joining right here via the YouTube join button. All right, let's dive in. John Williams' score once again kicks in. It's disgusting that they can use this score in such an atrocious film, but here we are. We have our standard Shark View heading through the ocean floor. Skiddy, dee dee, dee dee, do dee do dee, done done done done, do dee dee. Terrible Jaws title card kicks up and the excitement's gone before it ever really starts going and now we're having dinner with the Brodies. Lorraine Gary's back, baby. Reprising her role for the third time as Ellen Brodie. Okay brodie brodie brodie brodie what? I know you've been loving this Shark right here. We're now at the Police Precinct with the youngest son who took up the badge like his old man, who's prominently displayed in the background, a very comically large photo of him. Yeah, he's dead. He's been killed off unceremoniously in between films. Because of course, Sean takes out one of the patrol boats to unlodge some debris from a nearby buoy. Suddenly, he's viciously attacked. And by viciously attacked, I mean, there are several shots that are very frantic and you have no idea what's going on, blood sprayed, maybe one close-up of teeth, and then that's it. Sean falls to the floor, starts throwing a fit, and then decides, hey, I better hang out near the edge of the boat some more. And wouldn't you know it? Peek-a-boo, shark pops up, takes him out again. The dipshit goes down in two rounds. Skidding, dun, dun. Another brody bites the dust, and another one's gone, and another one's gone. Another brody bites the dust, and I'm gonna get to you. Another brody bites the dust. Look out. Boop, boop, boop, boop, boop, boop. After quickly confirming the kill, Ellen mourns with her family.   What do you think? Sorry, all right, she's a little, she's young. That's not her fault. It's the parents. Ellen's eldest son, Michael, consoles her outside before she kind of shoves him off and is like, listen, man, the shark's been after the family the whole time, man.  He's been meticulously waiting and plotting this. He's got a vendetta against our family. I'm at a loss. I don't even know what this means. They killed the Great White in the first film, and then again in the second one, and then they're not even in the third movie. And so I guess maybe there was some bad altercation with a third Great White with the Brody family. Is this a kid? Is this a disgruntled son of one of the first sharks that they killed? I don't know. I have no idea, but Ellen seems to think that's what's happening here. She did point out that Brody didn't die from a Great White but was in fact scared of one the whole time. So fear really got to him in the end. Some beautiful character assassination going on. Michael yells at her, not to believe all that voodoo mumbo jumbo. The voodoo thing was kind of an odd thing to say if you don't know the history of this film and the fact that it's based off a novel where a witch doctor puts a curse on the family and this shark is an apparition, a ghost of sorts that's haunting the family. Oh, it's fantastic. That makes more sense than what we have. Well, let's keep going. At the funeral, Ellen reminisces about once being in a good Jaws movie and how great it was.  What, why? Why the coloring here? Ellen's now on a boat with her family, ugly crying her heart out. They're headed to the Bahamas for a holiday. Now she's on a plane, flown by Michael Cain. That was a fun rhyme, I guess. Fun fact about Michael Cain here, he made $1.5 million for a seven day shoot in the Bahamas. Poor bastard, wonder how he survived it. His character name is Hogi and he's gonna show the granddaughter what it's like to be close to death as he goes up and down with the plane. Seems like kind of poor timing. Seeing as the Brody's just left a funeral for one of their family members, but you do you, Hogi. Ellen wakes up from a fever dream where she's attacked by a shark. So she has some PTSD for sure. She's trying to deal with things and it's not going well. Her son, Michael's out at sea doing science stuff. He was given a grant to study snails or slugs or who gives a shit, it doesn't matter. We're introduced to his buddy Jake, a fellow crew member who's super annoying and I hope gets eaten by a shark very quickly. All right, Michael's back with his mom, Ellen, who's once again yelling at him to switch jobs because it's that easy. It's that easy, mom, to just quit what you're doing on YouTube after trying to build up an audience for over a decade and just start something new. Let's just start over at him. It's time to give up, it's not working. Wait, what was I talking about?  He's going on vacation. That's right, he tracked down the Brody family from New York to the Bahamas, swimming just over 1,000 miles to find them because everybody knows that sharks have that ability. They just take in the scent of a person and then boom, it's locked in the data bank and they can just swim all across the ocean, finding them with ease. These are shark things. These are things sharks can do. Hogi's back in the mix, interrupting a beautiful sandcastle build. Very nice structure here. It's probably for the best though, as Ellen had just heard a shark growl. At that very moment, Michael picks up the binocs and he spies with his little eyes, Hogi putting the moves on the old lady.   Jake's underwater collecting a paycheck and I'm hoping the shark shows up to collect a Jake. We'll find out. And there he is. And oh my God, this is awful. This is genuinely embarrassing to watch. While this fugly puppet blob is ramming into a boat, Ellen's shark sense is tingling. She knows something's up and the reason she knows is because she's a strong female lead. And for the Jaws franchise, it's about time. Jake unfortunately survives the attack and Michael wants to keep this whole thing under wraps, especially from his mom who's preoccupied trying to get a Hogi inside of her. And no, I'm not referring to the sandwich. Meanwhile, Michael's wife is hoping to get a Hogi inside her as well as she flicks off her underwear right into her husband's face. This woman only exists in the film to be very frisky. Michael of course can't resist and he takes her right there. His mom meanwhile, gives Hogi a crisp handshake for the night. Michael Cain seems upset here. Hopefully the $1.5 million can console him later. We're now at a casino birthday party where Hogi just lost a bunch of money. That's okay, he has it to burn. During this sequence, we're treated to a mother-son dance where Ellen informs Michael she's done with the shark. That fish has failed and she's ready to move on with her life. But Michael's not. Back on the boat, Jake is super eager now to study the great white shark and he convinces Michael that they can spend a few days doing this. We then for some reason spend more time with Michael's hot wife as she scolds him for not taking out the trash. The takeaway here is she's once again, sexually frustrated. So they make sweet, fiery, passionate love right there in a welding room. Hot. Hot. This elegantly transitions to the crew, chumming for the shark. I'm chumming, I'm chumming. This is the opportune time for Jake to be taken up by the shark. Come on, you dumb-ass fish, he's right there.  The fin comes up. What is this shot?  This is real, this is real life? That looks like a blow-up. Did they forget they were filming on the day? Had intern Ben go over to the pool house, grab whatever flotation device he could find, blow it up and then just push it off to sea? Jake is able to successfully stick the rubber dildo with a tracking device. Presumably so the team is able to fully comprehend how a great white shark is able to conceive of who killed his family members, hold the vendetta for several decades and then track them across the ocean where he then can easily pick them off. It's truly impressive and bewildering at the same time. Hopefully they can get some data on this. Mrs. Brody's over the moon, chatting it up with Carla in her sex-welding dungeon about Hoagie. Cut to Michael who's now also woken from a fever dream about the shark and probably about signing up for this film which in turn was career suicide. We have a cringy callback scene in the kitchen where Michael's channeling the old man playing peek-a-boo with the little one.  It also really bothers me that right now Jake is at his place sleeping soundly in the comfort of his own bed instead of the belly of a shark. The next morning, calamity hits. Michael is attacked in his little yellow submarine but he might be singing a different tune once this affair is over. He swims into a sunken ship while the shittiest looking shark model I've ever seen slowly approaches. Michael suddenly forgets how to swim and slowly falls to the floor. We now have one single shot in this flick that looks pretty cool. Clearly the entire budget went to this one moment of the shark breaking through the side of the hull. That's it, that's it. Much like Eminem, Michael's not afraid to take a stand. He's going back in. Sometime goes by and it looks like he got himself quite the collection of seashells. Could have saved himself a lot of time and trouble and just headed on over to the local gift shop and picked some out of the bowl, but this works too. Beach day at the Bahamas is in full swing. Swimming, boating and even a sculpture contest. What else is going on at the beach today?  Thankfully, the shark gets confused for once and eats a woman that looks nothing like her. This sends Ellen into full-blown Ripley mode as she commandeers a boat and takes off after the creature. She heads out stag. Now the hunter becomes the hunted. Ooh, I can't wait for this movie to be over. Hogi and the boys get in his Cessna to catch up with the Mrs.  Which I imagine is a nod to what her husband said in the first film, which they will also bring up later. At some point, you would think the Brody's would realize standing near the edge of the boat, not a good look. An even worse idea, as the shark already pops up. Hi, but he doesn't even snap at her. It's just a tease. Oh, he should point out in this shot, it appears the Great White was animated by a child's claymation project. Hogi, now shot out of a cannon, smashes into the water with the Cessna, the boys get out, Hogi's still in the plane, but uh-oh, stinky, the shark's headed right to him. That's right, Jaws.  Some of the folks seem pretty concerned, but I think deep down, Michael wants this to happen. Never trusted the guy. You can't replace my father. Upon seeing this, Ellen has another one of her world famous fits, but thankfully it's short-lived.  In Michael's mind. Now really, Hogi gets on the boat, he's fine.  But then Ellen counters with the right hook saying it's not food this shark's after. It's revenge. She didn't say that part, but she showed up. With only 10 minutes left, dreams really can come true. As Jake successfully gets the device inside of the shark along with his own body. That's right, Jake is gonzo, baby. It's going down, I'm yelling timber. Jaws, now doing his patented roar that all sharks do, swims away with Jake still kicking and flailing under the water. Vintage Jaws.  Michael freaks out in this moment yelling, Jake.  They completely gave up on making this look like a shark. It's now just a giant rubber blob, slowly bouncing up and down in the ocean. Absolutely insulting. Michael is frantically trying to get the flashlight device working. Ellen is steering the ship, Hogi's being Hogi and the shark can be seen in the distance roaring its heart out. As all sharks do.  She smacks it away.   After some shock therapy, we're treated to the funniest scene in the film.  This prompts her to ram the boat into the shark's gut, which naturally makes the fish explode on impact as all sharks do. Blood and guts rain from the sky and the crew goes overboard. We get a shot of the shark, now ripped in a half, sinking to the bottom of the dark sea below. Michael resurfaces in what has to be two feet of water because he torpedo shoots upwards, like, you can't do that unless you are touching the floor or swimming super, unless he had like a jet pack underwater. He's not shooting up that high.  Bye bye, Jake.  He's alive. How? How? He was underwater for well over 10 minutes. Where was he hiding? Was he hiding inside the shark's belly?   Michael says he's going to be okay and they all live happily ever after. Jake meanwhile bled out in the hospital after several days of pain and anguish. He will not be missed. That's in my head cannon. He's fine too, I assume. Well, that's Jaws the Revenge, the final nail in a coffin of another film franchise that should have stopped at one. This movie has nothing going for it. It looks terrible, the characters are lame.  Truly remarkable stuff here. Let me know if you saw this movie years ago or just recently for the first time. Sound off in the comments below.  Subscribe if you haven't as I post tons of movie roasts, movie reviews, everything movie related every single week on this channel. And if you could go even further, share this video around with friends and family. Tell them about the show. If you really like it, become a Patreon. At patreon.com slash adamdoesmovies, there's different tier levels, one of which, Mythroll and Up, lets you pick one of these bad movies off of my letterbox to count and I will do it give you a producer shout out like my buddy, my friend, my brother, Colt & Oakwiss did. Alright that's the roast stay out of the deep end friends and I'll see you next time. Let's get...


You can't always get the win you want. Alright, go ahead, be a Bardock player. What? Haha, that was not what the situation I saw going down in my head, but that is fine. How's it going everybody? Dato Dui here, back with another round of Dragon Ball Fighter's rank matches, this time with a team of Goku Blue, Cooler, and Vegeta Super San. Uh, as most of you know, I really, really like Goku Blue. He's such a fun character. He's fast, a lot of teleportation moves, which is good, and then the team to back him up is just kind of random, honestly. But you know, also they help with the lockdown, like there, Vegeta catches a nice back dash, allows us to get Sel into the corner, and this is where Goku Blue just has a fun time. Alright, well, if we get, if we get goutered there, but that's fine. Again? No.  Oh god. Alright, this is Sel we're talking about. Ooh, Bardock assist catches us. I wonder if we could have gotten, I wonder if we would have won there. Maybe. Not really worth looking into now, because we got to change out. Oh, the assist. That's where Vegeta assist is super strong. Like ours would have been. Had he not gotten caught, too low is got to remember. Too low is there. Oh my god, the range though. Alright, guard cancel, Sel out. That's fine, as long as we can get Sel back. That was it. That was our chance. Oh, here we go. That's a decent enough chance too. Let's go ahead. Let's see that pretty little Sel. There we go. We give him an opportunity to put some pressure on, and then we just psych him out with Vegeta. Will he reflect? This is our turn. Let's take out Sel. Nice. Alright, so Sel is gone. Now we just have two more problem characters to deal with. That's right. We got a whole team of problem characters. Is he a Bardock player? No. That's a punish. Yep, yep, yep. You could have gotten a better punish, but this is still going to get us into the corner with a level three. Why? You were supposed to be an assist. That's fine. That maybe that's why you knew you could do something even greater. Oh, get that grab. This gives us a really good... Yup, yep, yep, yep, yep. Why not take the hard knockdown, you know? Why not go Super Kaioken? Alright, but what do we do with the knockdown? Is he a level three kind of guy? It doesn't matter. We are still in here. DP interlup. Whoa, he's that kind of guy. Oh my God, we got very lucky there. I got DP too. Never mind. We're not using that. Let's be real. JK, we got it. Oh, fell with him all the way down. Vegeta was with him every step of the way. He said up, up, up, down, down, down. Alright, let me hit you with an assist. What side did that hit me on? Oh, that was actually a good punish. That was good patience by him. Can we kill him here? Hey, down heavy gets the win. Alright, that was only game one. Kind of a messy game one too, but we'll take what we can get honestly here. Goku Blue didn't get to do any of his behind the back mixups, but there would be plenty of those to come. Surely back dash. Where's our Vegeta? Did he get hit somewhere along the way? Two lows, one, two. Wow, he mixed it up right when we were trying to learn. Oh, Super Dash comes out late. Oh, no down heavy either. Yes. Wow, and we got... Okay, I don't know how we got this side. Oh, Super Dash as well. No vanish afterwards. That's going to be a lot of damage. Potentially even a kill if he uses Vegeta's assist here. He does, and it is. Damn, he was pushing that kind of far. I was hoping he'd mess it up. I was like, push it, push it, push it. Oh, well, you can't always get the win you want. All right, go ahead. Be a Bardock player. That was not the situation I saw going down in my head, but that is fine. We accidentally actually used the Vegeta assist. Okay, I think he might have taken that on purpose, honestly. Oh, don't try to back dash against the man with the greatest range in the world. We got all this range, dude. Oh, is that going to be a knockout? Yes, it is. Cheesy sweep, and all we got to do is spend a Bard of Manish. That actually brings us back into the game. Aw, not quick enough. Oh, he was waiting down there like a shark. Dude, why do all Bardock players play like sharks? They just wait at the bottom, slowly menacingly clicking auto combo. Oh, let's go. You cannot get away. Okay, wow, we are trading blows. No, that was supposed to be a reflect, but I took my left hand off the directional stick. Go ahead, Cooler. Go ahead, scare him a little. Why not spark up? It actually hit. Wild. That actually helped us out so much. Please, whoa, whoa, whoa. Okay, I don't know why Cooler came out so slow. I thought that wasn't going to connect for a smooth second. All that's left of one Vegeta in our way. Wow, Rocket Leg. He is totally fine with playing this fast. Try to get a cheesy down heavy. I always go for it. Never works. You always want to see. Maybe it's this time. Is he going to level three in the air? That was really bad. That was me trying to read a Super Dash instead of react to a Super Dash. And we can all see how that went. Ah, okay, okay. Oh, keep in that corner. Let's go. Let's go. Oh, why did we try to advance? Oh, wow, wow, damage. Drop it. Oh my God, he did. DP, why did we forget about it? We forgot it. He didn't. He was mad. He was like, to be fair, I would have been doing the same thing. Can't believe we forgot about Super Saiyan Vegeta's DP. I was just playing that like he had a block. All right, rematch. Let's go back into it. Let's get it again. Run it back. Oh, that was so close. That was not how I wanted that to go, but equally as thrilling, honestly. Ah, you always want to apply pressure afterwards, but you got to watch the rogue Vegeta. Oh, really? No down heavy. Advantage. That's fine. Oh, you try jump. This is massive damage. Crazy damage. Oh my damage.  In fact, that's going to force my hand, dude. What am I supposed to do other than that? Okay, this actually worked out really well. It was going to work out really well if I didn't mistime that. Luckily, we still get the kill. I would have screamed if we did. I would have been, I would have been so disappointed with myself that we do all that range of the Vegeta assist. All right, get him to the corner. Let's go all the way. We're going all the way. That's the wrong move. That's the wrong move. That's the wrong DP. That was supposed to be the drop, but here we go.  Is he going to level three? Is he that kind of guy? No. Ah, he poked me back. He knew I was going to keep poking. He was done with it. He was like, stop, stop. He said enough. Level three, I would. Level one into level three. Damn, he wants Vegeta out. That's rare. No. No. Avoid the DP. Maybe it was a bit too obvious. Also, not that many Dragon Balls in place, so we can't turn back to that option. Okay, that was so bad, but we'll take what we can get, I guess. Watch out for the DP. Remember, screaming at myself here. Manage, vanish. No, it's not safe. Oh, but he didn't. He didn't leave us a window. Okay, we're out. We're out. We're out. Oh, he read it like a book. I think that situation played out exactly the same a couple of minutes ago in this very game.  We lost. It's all over. It's all over now. Oh, wow. That connected. Oh, my goodness.  He killed us. All right, two one to my opponent. Two one. Can we come back? Can we come back and win the set with this team? I think we can. Let's go ahead. Let's go. Let's try to focus down. Let's buckle down, use everything we've learned. Let's go. First, call out Vegeta. Then get hit by the B. Then get hit by the Vegeta. It's all going according to the plan. Why did I write the plan out this way? You would think I'd make myself win in the script. Again, that's not using what we've learned. That's actually using what's getting us killed. Superdass, there it is. Getting beat out on every corner now. There we go. At least we get a hit. At least we get the hit. That's all that matters in the long run. Oh, there we go. Dragon rush. I was afraid that I might have actually hit a button there. There we go. We get sell. Oh, baby. How to turn it all around. We're still leaking. Our team is still very much on the bad side. Oh, thankfully. Hit me. Hit me. Ah, I tried it, dude. I really did try it. Hit me. Hit me. Oh, that's if that's your plan. That's what you know you've lost, dude. Oh, the lows actually work out beautifully. Okay. I see you meet. All right. Well, we kind of got to get Bardock back. Okay. Okay. Okay. That's what I like to see.  This is the dream. I thought he was going to do the EX kick again. Wow, called me out. That was a read. Don't do it. Damn, DP, okay. That was serious. All right, but as long as we drag out this sparking, we should be fine. Okay, reflect, reflect, reflect. No reflect, but that's fine. Oh, no, no. Whoa, whoa, whoa. Cooler. Go ahead. Come in. Wow, that actually almost hit. Oh, there it is. Can't believe that didn't work, but whatever the Super Dash picks it up afterwards. That was a much better game than the one we had any time before this. Ah, but now it's 2-2 and we are still on our way up. We still have to be. This is still very much anybody's set here. No, no, no, no. Okay. Oh, the lows come out. All right, let's just pretend like we have confidence. Let's pretend we have confidence until we actually do. Well, that picked up cooler.  That was a crazy low and I respect that, but he didn't get anything too wild off of it. Level three, Kaioken. I should have went into three level ones now that I'm looking at it. Got perfect attack. He ain't Fenrich though. Wow, another read. I'm getting too obvious with these random changes. I know that sounds paradoxical. We're dead. Vegeta assist is dead unless he drops it, which would be a miracle. Please, please, please. Oh, yeah. Yikes, that's not good. Not good for the long run. I can tell you that right now. My cooler. Okay, let's try switching in cell. Really? No, the beam cuts right through the key blast. I was trying to keep him at bay with those. All right, let's go. Oh, we missed the luck. Okay, he dropped it. Oh, the Super Dash beats us out. I don't know if you guys can tell, but I'm losing. I'm losing the cool. The confidence has officially exited the building in exchange for Panic. Oh, I was about to say. Dude, these beams are really, this team has no good beams. We got coolers, hyah, but that's about it in terms of beams. Yeah. Yeah, I've done that so many times now. Getting red, the true story. Second to conduct. Whoa, my God. That was delayed as anything. Did he right up delayed it? He held it back. Get off of the bull.  Maybe with cells assist. Nah. Actually, yeah, you can right now. I tried jumping. I tried jumping and we lost, dude. Oh, well, that's going to be crew. That's that's what it comes down to. Sometimes, sometimes you get beat out and you just got to accept it. Great games to my opponent, though. It was a lot of fun. And we just got to take it and move on. Maybe this team wasn't it.  Hopefully you guys did enjoy this. Oh, if you have a favorite moment, make sure to let me know down below in the comment section. By the way, let me know down below in the comments if you guys are still into watching sets where I don't win. On that while you're down there, if you like this video, make sure to hit the like button and subscribe. I also have some videos up on your page right now that you can feel free to check out if any of them interest you. But other than that, I'm Dr. Doya. I will see you in the next one.


Don't sound very enthusiastic, but OK. So let's see. Last time, we talked a little bit about core black holes. I gave you the metric in excruciating detail in three different coordinate systems. And we talked about some properties, the metric, in particular, the ergo sphere and the horizon.  And I had given you homework. How many of you did your homework? OK. So the homework was to show that you have some geodesic equations here for a homework solution. So we had something like d z, or I'll just write it as d x d tau square plus gamma mu, say alpha beta, u alpha, u beta was equal to 0. And I was saying that this is not great because it's a second order system of differential equations. And we would like to rewrite that as a system of first order equations to do a first order reduction. And one way to do that is to realize that the energy, which is defined as t alpha, u alpha, the angular momentum, I guess I put till this on this last time, which is phi alpha, u alpha, quarter constant, q, which is essentially the killing tensor k alpha beta, u alpha, u beta, are conserved in the sense that these are constants of the motion. So d by d tau of e is 0, d by d tau of l is 0, d by d tau of q is 0. And in addition to that, you have the normalization condition for time like geodesics that u alpha is minus 1. So the goal was to use these expressions to find a geodesic equation that looks like t dot equals something, r dot equals something, theta dot equals something, and phi dot equals something. So the way to actually solve this is just write it out. So you have that u alpha is some vector. I'm going to call it t dot, r dot, theta dot, phi dot, where the dot means the relative with respect to proper time. And so then e tilde, for example, or minus e tilde is going to be the metric, alpha beta, t alpha, u beta, and that is going to be g t t t dot plus g t phi phi dot, OK? And similarly with l, right?  You'll have a similar expression. And here you'll have minus 1 is equal to a similar expression with t dot squares and phi dot squares and r dot squares and all of that. So then all you do is you have four equations for, in principle, four unknowns, t dot, phi dot, r dot, and theta dot. And you just algebraically solve that. And ta-da, it's not that hard, right? You can find these expressions in just standard textbooks. I'm not going to write them again. But as a corollary of this extra credit, I guess, I called it homework was to show that these things are conserved. So let's see. Let's write over here. So the idea was that d by d tau acting on e, say, I want to show that this is equal to 0, question mark. So I can rewrite d by d tau on e as the four velocity u alpha times the gradient, the covariant derivative acting on e. But e was t alpha. I put a minus sign here. So it's t alpha u alpha. I have too many alphas. Ah! So when I teach this in class, I just annoy my students whenever they say something like that. I just put a little tiny dot here. Now it's a different variable. So let's call it beta beta.   So this vanishes. And then you recognize that here you have the covariant derivative of a killing vector, doubly contracted with two copies of the four velocity. These two copies of the four velocities is a symmetric matrix, which means I get the same thing if I symmetrize on those two indices. By the contraction I can then just symmetrize on these two indices. But the killing equation, remember, is that this vanishes, which then means that this has to be 0. That this is 0. And the same goes through if you calculate it for q. And obviously the norm of the four velocities is also conserved. So those are some of the tricks that you are to employ when you're dealing with geodesics. So now, we've all warmed up for the type of math. We're going to be, yes. Can you repeat that question? Because I have to repeat it to the thing. I couldn't hear you. Yes. So the question is, can you always show that the equations are separable in this sense of superability if your background is stationary and axisymmetric? And the answer is that that's not always the case. So for example, there's modified theories of gravity where the current metric is not a solution to your field equations. And in that case, the space and it's still stationary and axisymmetric in the sense that there is a conserved energy and there's a conserved angular momentum. And the norm of the four velocities is still the norm of the four velocity. But you can show that there is no second run killing tensor. So without the presence of this Q, you can't even start following this proof. So the issue of separability of the equations of motion is very tightly related to the petrope type of your spacetime. And proving that your spacetime is petrope type goes beyond just saying that it's stationary and axisymmetric. And it depends on the theory and the field equations. So talk to me about it later if you want because that's like a full lecture. OK, good. So now that we've warmed up, let's look at Emory's. So an Emory is defined as a definition. I'm going to do it the math way. It's a stellar mass compact object. So stellar mass compact object in my life is abbreviated as SCO because I don't want to write that a million times. In a generic, I'm going to say in spiral or orbit, around a supermassive black hole. So there are two acronyms for you. Stellar compact object or stellar mass compact object and supermassive black hole. So that's our definition. So even though a lot of what I do has to do with calculating these orbits and calculating the gravitational waves emitted by such systems, I think it's always important to remember like what sort of astrophysical scenarios could produce these binaries. So we're going to do like two minutes of astronomy. So just bear with me. So there's two, so formation scenarios. There's two classic formation scenarios that you should know of, and these are sort of fairly lengthy topics. So we're going to do it fairly briefly here. So the first scenario is called the capture scenario. And here's the idea that you have a galaxy. We're going to do formation scenarios with pictures only. So it got me my colors over here. So galaxies are orange. Everyone knows that. So here's my galaxy, and everyone knows that supermassive black holes are blue. So here's my supermassive black hole very much not to scale. But I was told that if I don't draw big, you can't see it. So imagine that you have some sort of binary that's over here, and it's going around this. Imagine like it's going around. Like that, some binary of two compact objects that are both small, like stellar mass, black holes, maybe something like that. But as you can imagine, galaxies have tons of stars, and there's tons of processes that occur in the galaxy that can affect the dynamics of my little two stars. See, unfortunately, we like to solve the two-body problem, but in real life, there are more than two bodies. And there's also more than three bodies. There's like a gazillion bodies. And so every now and then, it can occur that this binary will interact with a third object. The third in this chord is going to be painted purple. So here is the bad guy. And the bad guy interacts with this binary. And the end product of that interaction can be that the disturber here becomes bound to one of the components of my good binary. And now these two go around. And the other component of the binary is sort of ejected. And there is a probability that that ejected component will be headed toward a galactic center. And if that's the case, eventually it will get close enough to this supermassive black hole that it will sort of loop around. And this distance might still be very, very large, right? So this is not a small distance. But what happens is that in the process of coming with a small impact parameter to the supermassive black hole, this small object emits gravitational waves, which everyone knows are white. And when that happens, the binary formed by the small compact object and the emery, which where this binary in the orbit was very, very large, the seven major axis is very, very large, becomes much more bound because now that orbit has lost a lot of energy in this burst of radiation that it emitted. So what happens now that instead of this one going back to its initial trajectory that's over here, it becomes bound, bound to the supermassive black hole. And you might think, like, this is incredibly unlikely. But it turns out that if you take a probability that's really, really tiny and you multiply it by a gazillion, which is the technical word for the number of stars in a galaxy, then you get a number that's finite. And the particular value of what that number is, like how many events like this happen inside of some volume centered at the solar system per year, nobody knows. There's very complicated astrophysical processes and there's rates. So there's the rate of how often this would happen and they range from zero times per year to like a thousand times per year for systems that would be detectable with gravitational wave instruments in a decade. How are we going to be able to figure it out? Well, either someone really, really, really smart is going to put in all of the physics that are needed to solve this problem, maybe on supercomputers and calculate it and convince us this is the right number or much more likely we'll turn the instrument on and we'll measure and we'll see, like, ah, the answer was 11. Okay, so that's one formation scenario. Another formation scenario is, what did I call this one, disk formation. This one is less likely than that one but let's describe it anyways. Okay, so in the idea of disk formation, what you have, you have your supermassive black hole which, again, is blue, a lot of galaxies that hold supermassive black holes tend to have accretion disks around them. Those accretion disks need not always be perfectly thin disks like we like to imagine, but a good chunk of the time they are or they're expected to be. So let me draw a disk.  So here's the disk. Imagine that the disk is thin, like a thin disk. And there's a lot of gas here and maybe the disk stops some distance away from the horizon. That distance might be the innermost stable circular orbit, it might be a little bit closer in, doesn't really matter. Point is that this disk has an enormous amount of mass but in any particular region of the disk there's very little density. It's because the disk is gigantic. Okay, so it's very small density but then you integrate over a large volume, you get a large mass. And what can happen is that in the outskirts of the disk the gas that is present can fragment and form stars. Just like stars are supposed to form, say in the solar system, right? You have a giant molecular cloud and it's all collapsed and they're fragmented. Pretty as a little star. So this star, this sun-like object but more massive maybe that the sun-like object is gonna be moving around here, it's gonna take forever. Eventually, it's gonna migrate also, it's gonna migrate when we say migrate we mean it's gonna move in closer to the black hole. Slowly, very, very slowly because it's very far away. Not due to the emission of gravitational waves, has nothing to do with gravitational waves. It migrates in because it's immersed in a disk and as it's moving around there's viscous drag because of interactions with the material but also the object produces little ripples, little waves on the disk and those little waves on the disk carry away angular momentum which then back-reacts on the orbit by pushing it in a little bit. Eventually, if you wait a long, long, long time, this star can go supernova. Supernova is red, ka-poof, okay? And if the original object was massive enough after it goes supernova, it can live behind a black hole. So after this explosion, now we have a little black hole.   You might disrupt a little bit of the neighborhood of this disk but this will refill very, very fast. So if you wait a little bit longer, it's like nothing happened but now you have a black hole.  What's gonna do what black holes do? Which is just go around. And eventually, just like the star was being dragged into the supermassive black hole, this object will slowly move closer and closer in until eventually it enters the gravitational wave-dominated regime. And now you have a memory. Okay, so I don't work on formation scenarios because I'm not an astrophysicist so please don't ask me questions. But I think it's important for all of us to know what the formation scenarios that people have in mind are for the models that we are trying to solve for. Like so that we know that this actually are supposed to happen in nature, how they're supposed to happen in nature. And if you wanna read more about this, there's thesai after thesai that have been written about it. Yep. No, is there no questions? Yeah, yeah, very good. So the question that Bolo asked is, it is important that the object be compact. That is, it did not be a star for the definition of an embryo. Why is that? That's a very good question. Here we're dealing with supermassive black holes. So certainly if the supermassive black hole has its masses like 10 to the six, 10 to the seven, the tidal force that it exerts on a companion, say when the companion is at the horizon or closer to the horizon, is actually very small. Why is that? Because the tidal force goes as the Riemann tensor and the Riemann tensor goes as the mass of the object divided by the separation, say cubed. Okay, so if your separation is roughly the horizon, so M, then M over M cubed is one over M squared. And if M is giant, then that force is very weak. So you can certainly have a star go right through the horizon. Don't even notice that there was a horizon there.   The reason that we don't consider that is because the strength of the gravitational waves that they will emit is much, much smaller than the strength of the gravitational waves emitted by a small black hole going into a supermassive black hole. Because the gravitational waves' strength scales, if you wanted scales with a mass of the objects, but when they're black holes, but when they're stars, they scale essentially with the density of the object. So, okay. All right, so with that short explanation in mind, let's now talk a little bit about modeling. So, modeling. So I like to describe this modeling of, so what are we modeling? We're modeling the gravitational waves emitted by this emrys, okay? And so to understand the gravitational waves, you're going to understand the motion. Unfortunately, the problems are coupled, so we need to understand the motion and the gravitational waves at the same time. So the way I like to describe this is through this very nice diagram that I first saw right down, written down by Lior Barak. So Barak has a very nice review article. That you can all read. So Barak is a professor in Southampton, Lior Barak. And I think it's CQG 2609. There's others, Eric Poisson, the same Poisson that wrote the Poisson Toolkit book and the Poisson and Wheel book at all. He has a living reviews in relativity, LRR 14 from 2011 also. So these are your references if you want to read more about it. But in any case, let me plot, I don't want to plot this, okay. Let me plot on this axis, the orbital separation R divided by the, say, total mass of the system or the mass of the supermassive lacool. Let me plot here the mass ratio. So the mass of the small compact object divided by the mass of the big object or the total mass, it doesn't matter. And so the mass ratio ranges from zero to one. That's the domain. And the separation ranges from when the thing merges. So maybe not zero, but whatever you want to call it, the horizon, I'm going to call it zero. It doesn't really matter. To all the way to spatial infinity, right? And so in this domain, what I want to understand is what approximations can I use to solve for the trajectors and the gravitational waves? Or what methods can I use? So you see, if the mass ratio is very close to one, well, the first thing I'm going to say is like, I know. This is all nonsense. Just throw it all into a supercomputer. Let the computer deal with it. I'm going to have to worry about it. The problem is that if you have one of these extreme mass ratio orbits, the amount of time it takes for the orbit to adiabatically shrink by a little bit scales inversely with the mass ratio. Okay, so if your mass ratio is very, very tiny, you have to wait a very, very long time for the gravitational waves to react on the orbit and for the orbit to shrink and for the system to merge. On top of that, if you have an extreme mass ratio in this spiral, you have to model in your numerical grid not just the supermassive black hole, which is actually pretty large, but also the small compact object. So you have to resolve the compact object, which again, that resolution, the difference in scales is again of order to mass ratio. And on top of that, you have to then also model the gravitational waves that typically have a wavelength that is much larger than the size of the small compact object. And that needs to be extracted very far away from the binary system. So all of that means that if you actually try to push your numerical simulations to the embryo regime, which is over here, you are just out of luck. Okay, so there's some sort of limit as to how well numerical relativity, not how well, but some limit on what numerical relativity can do today. Okay, some bar here. On top of that, even if you're considering comparable mass binary, so like two black holes, equal mass, if you put them really, really far away from each other, then the amount of time they're gonna take to spiral in, it's gonna be enormous. And you only have as much time to run your codes as the lifetime of a grad student thesis. So that puts a bound on the maximum separation, which means you cannot really go all the way to spatial infinity, because then your grad students don't graduate. Okay, so then that defines some sort of regime here where NR works wonders if you actually work on it very carefully. And this goes back to Pewter's talk, where in order to do the numerical relativity problem, you have to take your space time and foliate it with space like hypersurfaces and do a three plus one decomposition and then ensure that your constraints are satisfied, blah, blah, it's all very complicated. It's all very cool, it's all stuff I'm not going to talk about. Then what else can you do? Ah, so Pewter talked about the post Newtonian approximation, right? He was actually talking about the post Minkowski and approximation. It's an expansion in M over R or in weak fields. If you want in capital G, the strength of the coupling constant of the gravitational interaction being very weak. But on top of that, you can also use an expansion in small velocities. That expansion of the small velocities is also sometimes called the post Newtonian approximation. I'm going to talk about that tomorrow on my birthday. I might add. You're welcome. That's okay, because that's like what I actually do. So it'll be easy. But of course, as the orbital separations become very, very small, the strength of the gravitational interaction becomes huge and the orbital velocities can become actually not much, much smaller than the speed of light. So clearly, these post Newtonian approximations cannot work when the orbital separation or the velocities, when the orbital separations are small or the velocities are large. So there must be some different color. Pn is blue. There is some minimum regime here, some line below which I cannot go with my post Newtonian approximation. So, but I can go all the way here. So you would think that I can extend this all the way to like tiny mass ratios. Okay, that the post Newtonian approximation, expansion in velocity will work even when you have a tiny, tiny object going around a supermassive black hole, as long as the separation is large. It turns out nobody fully understands this. So math people, you're welcome to work on this if you want. That the properties of the post Newtonian expansion that has actually been taken to what we would call in physics, three loop order. So that's an expansion that has been taken up to V over C to the seventh power relative to whatever the leading order term was in the expression that you're trying to calculate. Okay, that's a very high order perturbative expansion. So you can look at the convergence properties of this series. And you can try to study, well, you can try to understand whether that series converges to something as you add more and more terms or whether that series is asymptotic or divergent. And we don't know, we don't know for sure whether series asymptotic or not. What you do know is that as you look at more and more extreme mass ratios, the coefficients in the series become larger and larger. Which is suggestive that an approximation that might have been okay over here if you fix the order to like V over C to the seventh might not be as accurate if you increase the mass ratio, if you make it more extreme. So it turns out that for the purposes of observation and for modeling, the Poisson-Gener approximation is not really valid or accurate enough as the mass ratio goes to zero. Okay, great, so boop in. So what can we do now? Well, anyone wanna guess what's the obvious perturbative scheme that we can use? I love it when audiences are very participative. Argentinian guy, what you gonna do? Very good, I was not going to talk about that, but no problem. So yes, these are essentially Taylor expansions in V over C, okay? So you might ask, well, we know what to do to improve the convergence properties of a series. We resummit, okay? So there's ways in which you can resum these expansions and one way that's very, very clever and very effective is the so-called effective one body approach. You can think of it as a resummation. That tries to make post-Newtonian, which I forgot to label, more and more accurate if you want more and more valid in this regime and actually in this regime too. Like he wants to push this line to the left and this line down, okay? But no, what I meant is, what do we do here? How do we solve the problem here? Waltz didn't. We do black hole perturbation theory, right? We expand our problem in Q much less than one, okay? And that's a good parameter to expand because unlike the velocity which changes as your orbit evolves, Q doesn't change because, well, it changes because objects could accrete a little bit of mass energy. But for the most part, the mass is essentially constant so Q is essentially constant. It's a good expansion parameter. So here's where cell force calculations or black hole perturbation theory calculations are done. Now, do not go and tell your friends, oh, Nico told me that these are the lines and I can sort of infer that this is zero and this is one, this is like 0.25 and this must be 0.6. Like clearly where I drew this line, it's a cartoon, right? Like nobody knows where these lines are. Like at all. So it is entirely possible, but we do know that positonium seems to agree with numerical relativity in this regime from the comparisons that have been done. Especially when you resum them. We also do know that cell force calculations seem to work or seem to reduce to the post-Newtonian results if I take the cell force calculations that are just solutions in Q much less than one and then on top of that, I do a post-Newtonian expansion, a V over C much less than one expansion. Then if I do those two expansions here and then I take my post-Newtonian one and I do an expansion in Q much less than one, then those two bivariate expansions match. So that's good. And there have been comparisons between cell force calculations and numerical relativity simulations in some regimes, but it's not clear how well those two match because NR can't really go here. Okay, lecturers are not allowed to ask questions. I'm kidding. Yes, correct. Excellent. So let's explore that idea because that's exactly what we're gonna do. Thank you. It's like I planted that question. Okay, so historically there have been many, many ways in which you could try to model M-RES using a Q much less than one expansion. I am going to explain this or present just a few of the methods. There is no time to present all of the methods. All of the methods are approximate in one way or another. Some are way better than others in terms of like accuracy of your approximation. So let me first show you the methods that are least accurate, but easiest to understand. And hopefully before I'm done, I'm gonna be able to derive some of the equations that are used in cell force analysis. So now I need to cheat because otherwise I'm gonna get the equations wrong. So let me begin with the cladgiest of the cladgiest approximations. Sometimes called the semi relativistic approximation. I felt like I had to describe this because it was pioneered, well, because I'm in Italy and it was pioneered by Remo Ruffini. So I figured if I don't mention Ruffini at least once then people are gonna get mad at me. Bigger font. Yes, Ruffini and Sasaki. And they have a very, very beautiful paper in PTP progress in theoretical physics. It is a Japanese journal, 66 from 1981 that you can refer to, very readable. So what they said is, like Peter was saying, like if q is zero at that point everything is just a geodesic, right?  And so the four velocity of the small compact object is gonna be represented by the background solution which is the four velocity of geodesic motion plus a small correction to that trajectory. And in principle you could go to higher and higher order. So the equations that you need to solve remind you are, guess I'll write them over here because they're always going to be the ones we are going to solve. g mu nu is equal to eight pi t mu nu, g and c are one. And obviously, conservations of stress energy tensor, okay? So in the words of Wheeler I suppose, at least as far as I know, matter is telling curvature or spacetime how to curve and then the curvature of spacetime is telling matter how to move but these equations are obviously coupled so you need to solve them sort of simultaneously. Now, if you neglect, if you do this expansion and you plug it into these equations then you get that too leading order. This background metric has to just satisfy the vacuum mines and equations without a source. And that's just the current metric. So yay. And in the absence of a small object then that source, that current metric is stationary, it's not moving anywhere. So to essentially first half order higher than that I'm gonna have a point particle which is how I'm going to describe this more compact object moving or a test particle moving in the background of the current metric. Which then gives me what Peter was saying the geodesic equation for the point particle. But then what I need to know is okay now that I have that point particle the test particle moving in a geodesic how does it back react on the metric to generate the gravitational waves? So I have to go back to here and now I have to put on the left hand side that the metric is the metric of a black hole plus a preservation H and I have to put in on the right hand side that now I have a stress energy tensor and that stress energy tensor is that of a test particle and that test particle is moving with a trajectory or warline given by the solution to the geodesic equations. And so if you do that you'll find so equation one one becomes box on H mu nu trace reversed in this case equals a minus 16 by T mu nu after we use a particular gauge condition which again, Peter was calling the wave condition wave coordinates turns out that that particular coordinate system the wave coordinates that satisfy box X equals zero imply when you do a perturbation about Minkowski the gauge condition that D mu on H mu nu equal to zero with a particular definition of H I can get into this later if you want I probably have to describe it when I talk about post-Newtonian tomorrow. So in their approximation, what they said is in order to solve this equation to make things even easier we're gonna say that this box operator which is supposed to be a G mu nu covariant mu covariant nu we're gonna replace for G mu nu and for the covariant derivative the back that them in koski metric so we're gonna make the approximation that just when I solve this equation just when I solve that equation that the background is Minkowski okay and if I do that then oh and I'm also going to say that T mu nu is that of a point particle or a test particle so you have some mass for the small object and then the four velocity mu mu nu and then a direct delta function for dimensional of the coordinates X row minus zero of tau theta if you do that there's also many questions okay yeah yeah so that's what I was trying to say I went through it a little bit fast so if you actually do this calculation properly you realize that this is not the only term you have if you do a perturbation about the car metric you also have a term that depends on the Riemann tensor and this will be the box of the car metric so the approximation that Sasaki and Rufini did again this is the clugiest of the clugiest models okay it's just say well when I have the linearized equation I'm going to replace what was the super massive black hole background with a flat Minkowski background which is totally wrong but we're gonna do it anyways okay so if you do that then the Riemann tensor is zero and then this is the box of Minkowski and that's good because I think if this is the box of Minkowski I can invert this because there's a well-known Green's function for it yeah so the matter field is that of a test particle that has a mass M and it's in motion with some four velocity like so that is localized as a distribution plus of matter hmm sure let's give it that name it's a test we call it a test particle in physics yeah so I didn't quite say that explicitly this is the trace reverse metric perturbation so it's H mu nu minus one half eta mu nu times the trace of H calculated with a Minkowski metric yeah so that trace reverse is computed from the eta trace okay so then if you do that turns out you can solve that you can you know the solution to that equation is very easy well G mu nu H mu nu is going to be minus 16 pi box to the minus one of this and then I'm done right supposed to be a joke and okay so you use your Green's function and you turn up you end up getting and it looks like minus four M times the distance to to your field point where you're calculating this times U mu U nu divided by a vector L alpha U alpha and all of this evaluated at retarded time so retarded time is t minus t minus r if you want a field point r leave it like this to retarded and L alpha here is the vector one times the n unit vector that points from the field point to the location of the small compact object or vice versa actually small compact object to the field point and U mu here is a four velocity which you write as gamma some Lorentz factor times one comma three velocity and presumably you have this because you've used your geodesic equation to solve for the velocity of the test particle so what is this solution what do we call that solution in physics yeah it's the linear feature solution for radiation so it's B card I don't know how you pronounce these things solution of electrodynamics for a particle that's moving on a flat background that's a good question so so in practice we tend to write these things in in coordinates that are adapted to the Minkowski background okay so because there's the box of Minkowski so we typically use for numerical reasons just Cartesian x y z coordinates if you can use spherical coordinates if you want but then numerically you get into issues sometimes when you hit the poles because you don't know how to evolve so you have to be a little bit careful about that but yes they have to be adapted to the background good nobody liked the solution but it's a solution from the 80s so you know now we're going to accelerate 10 years I'm going to show you a less cludgy waveform called the clutch waveform or Cluj depending on how you pronounce it I pronounce it clutch so this is an idea so the the idea here is like let's try to come up with some sort of approximation that solves these equations but a bit more accurately right like you don't want to be using you don't want to be using this cheat this incorrect step of throwing away the background completely it's going to be totally off so so how do we do it we do it as follows we go ahead and we again follow what Peter was saying earlier so at zero's order in Q leading order in Q when Q is zero then I should have a test particle moving in a geodesic now that geodesic is going to have some so to leading order I'm going to have a geodesic it's characterized by some energy I'm going to momentum and Carter constant okay so let me draw a two-dimensional this is a three-dimensional space right and Q let me just draw it in two dimensions let me suppress Q for now so E and L so I can pick a point here some initial condition for my geodesic I just pick an orbit with some energy and some angular momentum and that's just a geodesic if I run a computer it'll just go around forever and ever and ever if I pick E and L very very intelligently I can even make that orbit be a circle so but I could have picked another point this would be another geodesic and another geodesic and another geodesic and another geodesic these are all different geodesics look at my beautiful grid of geodesics so I've gridded this phase space okay so what happens in reality is that if I start with some geodesic I start my evolution here somehow that geodesic needs to evolve and spiral into the black hole why is it spiraling into the black hole because the geodesic is disturbing the space time and that generates gravitational waves the gravitational waves carry energy and angular momentum and current constant out of the system which then back reacts on your orbit forcing it to spiral in forcing the E, the L and the Q to change in response to the emission of gravitational waves so there has to somehow be if I'm here some way to compute how how E and L will change due to the emission of gravitational waves in a small neighborhood of that phase space point so if I can do that I can compute like a little arrow okay and if this grid is very very dense this is not trying to scale so let me just draw it like this it's an arrow I could then jump from here to here to this other point and then there I can go and I can solve my geodesic equation again and calculate my rate of change of E and L and Q due to the emission of gravitational waves and calculate another arrow so let's say this one takes me this way so I jump so I jump to some point here and I do it over and over again computing little arrows that will take me hopefully through phase space from geodesic to geodesic to geodesic okay and then you join the idea is that you join all of these geodesics together to get the full trajectory okay ask me again in five minutes so what we're doing here is something that it has been known in celestial mechanics for a very long long time it turns out it's called um oscillating orbits so the idea is that here I have an orbit that's a circle and then I am losing energy and an angular moment well that's just I'm losing energy such a way that after I lost enough amount of energy I turn into some sort of other circle there's some limit that you can take in which this geodesic sort of oscillates onto the next geodesic and then oscillates onto the next geodesic and so on and so forth sort of like shrinking slowly from one circle to the next circle to the next circle so this was an idea that was put forth for a variety of people but the reference that I typically follow for this is Hughes prd 2000s I think there's two papers or he explains this thing so the main bit that's missing here is how do I calculate e dot l dot and q dot right how do I calculate if I have a geodesic how do I calculate how much how much the energy and momentum of the current constant change due to the emission of gravitational waves so you need to prescribe somehow e dot l dot and q dot and there's a couple of ways in which you can do that one way in which you can do this is by saying I'm going to use the post Newtonian expressions for e dot l dot and q dot so expressions that are only valid in the small velocity limit again totally wrong because the geodesics are not necessarily slowly moving but you can certainly do it and see what happens so option one option is you can do p n a better option is you can use something called black hole preservation theory which I'm going to describe on Thursday to calculate something called psi 4 which is one of the Newman plan road scalars and that's psi 4 you can eventually show it can be used to calculate the amount of energy carried out by gravitational waves at spatial infinity okay psi zero would allow you to compute the amount of energy absorbed by the black holes as the waves go into the horizon so that's another way in which you can compute this okay so this is sometimes called the sort of frequency domain method for calculating because there's a frequency domain method to calculating this psi 4 the post Newtonian prescription of these variations of constants is much much more kluge but definitely it's something that people have done in the past so that's method two and if you want if you want something that's more complete what you can do is remember that you have expressions for t dot r dot you know theta dot and phi dot right into one from for geodesics that's how I started my entire lecture and these things were functions of the coordinates but there were also parameters e and l and q here which were supposed to be constant and the same thing here and the same thing here and the same thing here so what you could do is if you have some sort of analytic way to prescribe e dot and l dot and q dot say from post Newtonian theory then instead of just solving these equations numerically on a computer you can solve these equations enhanced by these equations which now means that your constants are no longer constant but they're varying on a different timescale but they're varying so if you solve if you do that then that's another way of implementing this idea of escalating orbits okay so in my last 15 minutes let me tell you why all of this is completely wrong and let me tell you what people have done to fix this problem or fix the problem with these approximations okay so who can tell me what's wrong okay who can tell me one thing that's wrong no need to list everything what have I not included when I do the calculation this way the cell force what is the cell force right so the small object is right so the small object is not a test particle and because it is not a test particle it curves space time and because it curves space time the curvature that it presents on space time actually back reacts onto its own trajectory and that effect needs to be taken into account sometimes that effect is called the conservative part of the cell force because it's symmetric and they're time reversal for example it's if you want the part of of the force that comes from the space time metric or from the curvature in the space time metric produced by the small object and this thing that I'm calculating here e dot and l dot and q dot they are essentially also producing a cell force but it's a dissipative cell force okay it's telling you how how your geodesic is not really a geodesic but it's the trajectory is forced if you want by some sort of radiation reaction force okay so this includes some part of the dissipative cell force but we want to include the whole thing so cell force and if you have questions think Boggs in the audience and he can tell you how he derived these equations a long long long long time ago better than I can um all right so so this is this is my derivation of this thing so a this is a non very much non rigorous derivation of this thing what is it that you called it Peter it was a very dirty proof of how you do this result right anyway so so what is the motion that you're trying to consider the motion you can write it down as the second derivative of the trajectory plus some gamma prime alpha mu nu d z mu d tau prime d z nu d tau prime equals zero where primes here denote the trajectory on the spacetime g mu nu which is equal to g mu nu of the supermassive black hole plus a correction h mu nu due to the small compact object so if you want if you knew how the small compact object is curving spacetime you could in principle then take that metric whatever that metric is and plug it into here into the Christophels and and calculate and calculate the geodesic equation on that background so this goes to what you were saying earlier so you can think of this as the geodesic or geodesic motion in a perturbed background that's one way to think about it another way to think about it you can reinterpret this as you know geodesic motion so no primes now which is now not equal to zero but it's actually equal to some force f alpha that I'm going to call the self force and for good measure to make the unit work let me multiply the whole thing by m the mass of the small compact object so you reinterpret this as a trajectory on a background that is just the background of the supermassive black hole but that is forced okay so these these two descriptions one of a trajectory on a perturbed background versus one of a trajectory in an aperture background that is forced can be made essentially equivalent so what you do now what you do now is we're here is you what we want to do is we want to calculate what this self force is so so what is the self force is f self force so we do some change of variables you know you know that d by d tau it's going to be equal to just d tau prime d tau d by d tau prime and similarly for the second derivative it's going to be two terms in this case okay and so we go back to this equation over here which I'm going to call equation two and so equation two can be written as let's say m times d2 c alpha d tau squared d tau prime over d tau squared plus d2 tau prime d tau squared d z alpha d tau prime plus the second term which I'm not going to touch m alpha mu nu d z mu d tau d z nu d tau okay so all I've done here is I have replaced in equation two d by d tau squared by something that depends on d by d tau prime this should have been a prime here sorry yeah so there's two terms here so if I apply another d by d tau there's going to be one that acts on here and it's going to give me d2 tau which is the last term and another term is going to oh I don't see what you're saying so this what I wrote is this here no no so this is correct so all I've done is I'm rewriting this equation so I am not going to rewrite that in terms of tau prime so that's correct okay so just doing it in steps so just give me a second so what I'm going to do now is I'm going to use that d2 z alpha d tau prime 2 is given here by equation 3 by this expression so I can rewrite this as minus m gamma prime alpha mu nu minus gamma alpha mu nu times d z mu d tau d z nu d tau plus this second term d2 tau prime d tau squared want d tau d tau prime d z alpha d tau so after you manipulate things a little bit you can see like for example this last term here the second term is appearing right here this term over here comes from from there and so this term over here is the second term in parentheses over there and so now you notice two things one thing is that this is the difference between two Christoffel symbols calculated in essentially two different spacetimes one is a spacetime that is not perturbed and another one is a spacetime that is perturbed so when I calculate that difference the difference is just going to depend on covariant derivatives of the perturbation because the covariant derivatives on the background are going to cancel the other thing you notice is that this term over here you know it depends on on d z alpha d tau but d z alpha d tau is a four velocity and you know that the equation two you know that equation two is saying that f s alpha written in terms of the four velocities u mu d mu u alpha and if I dot this whole thing with u alpha then this right hand side is zero because u alpha u alpha is normalized to minus one so u alpha times f cell force alpha is equal to zero which means that the only part of the cell force that we sort of care about for this derivation is the part that is perpendicular to alpha to u alpha okay so this piece here must be containing a part that's perpendicular to u alpha and a part that's parallel to u alpha and the part that's parallel to u alpha at the end of the day must be canceling with this term so since we only care about the part of u alpha that is perpendicular as a part of f alpha that's perpendicular to u alpha we can project which we're going to do now and so the projection of f alpha cell force is just g alpha lambda plus u alpha u lambda so we project perpendicular to u alpha and you end up getting minus one half m g alpha lambda plus u alpha u lambda times times covariant derivative nu h lambda mu plus covariant derivative mu h lambda nu minus covariant derivative lambda h mu nu where these covariant derivatives are associated with the supermassive black hole background so the kermetric okay and this whole thing is sometimes called m times covariant derivative this is defined to be m times covariant derivative alpha beta gamma acting on h beta gamma we're going to do a piece of the cell force which is what you care about so now now you're almost done because um well you are essentially done what you need to do to solve for the trajectory of the small compact object is to solve this equation over here this is a geodesic that is being forced by this term over here so this is to first order so it's going to be the supermassive black hole background remember that's also the covariant derivative associated with the background so you can calculate all of the terms here but of course this thing also depends on h so you need to have some sort of prescription for what h is so if you do properly an expansion of the Einstein equation about a curved background smbh plus h score what you get is box of the trace reversed metric perturbation plus two times the Riemann tensor mu alpha nu beta acting on h bar mu nu equal minus 16 pi some t alpha beta for your matter source and again here box is supposed to be box of the background and r the Riemann is supposed to be the Riemann of the background so now you have two equations that are coupled one for the metric perturbation and one for the trajectories this is not the equation for the trajectory the equation for the trajectory is equation two with f-cell force this thing and now we're done right easy peasy right so bob solved this in do you remember when this was on 70s 80s still in my thumb there bob okay did but do you remember the year this time okay so what I was going to what I was going to ask the students was like are we done like is this is this it and the answer which bob already gave you that no this is not it because that h mu nu is singular at the location of the point particle or has a piece that's singular at the location of the point particle so you need to figure out a way to resolve this this issue so problems just over here and this is this will conclude my my talk running almost over um so small in quotation mark problems so one your test particle has a divergent self-filled at the location of the small compact object other little problem delta functions their distributions are not strong field representations uh say point particles and so on and so forth so the reason is that if you actually take a bowl of matter and you compress it more and more and more and more and more to turn into a test particle then at some point the energy density that's contained inside of this body will become so so large that that particle will collapse into a black hole by something called uh the hoop conjecture which you can read about you want by thorn in the 70s so the resolution there's well there's different ways in which you can you can show this result but one way is to treat the small compact object as a black hole treat the skull as a black hole and use my favorite mathematical technique which is asymptotic matching so here what you're doing is you're solving for the problem in a neighborhood that's very very close to the small compact object and then in an area that's farther away from the compact object and then there's an overlapping region of validity where you just match the two approximations and if you do a calculation correctly you discover that the cell force really is not m times d alpha beta gamma acting on h beta gamma but rather it's m d alpha beta gamma acting on the regular part of h beta gamma where h mu nu has been decomposed into a singular part plus a regular part which by regular here we mean a part that doesn't diverge the location of the test particle so um this sort of expression with the regularization including is what Bob was referring to as the mi sa ta ku equation which stands for mino sasaki tanaka queen and world equation um so I leave it there there's a lot more work that uh I had to close over for obvious reasons that goes into exactly how to extract this regular part of the metric perturbation a lot of these calculations are numerically so subtracting a singular part is quite tricky there's gauge issues blah blah blah metric reconstruction um so this is a very hot activity of research and by the way this is just the first order in q and we need everything then just second order so good luck with that fortunately I am not working on that so I'll stop there thank you