Please feel free to not hear this talk by leaving or paying attention to something else. So this is the title of my talk Stability of the Kerr-Koshy Horizon and the Strong Kosmic Censorship Conjecture in General Relativity. Let me immediately give you an outline of this talk. So first and foremost this talk is really about the inside of black holes and a big conjecture in general relativity which in some sense is motivated by the behavior of black hole interiors. So a few weeks ago I gave a talk about aspects of the stability problem inside and outside of black holes and I ended up talking mostly about the outside so this talk will be only about the inside. So this talk is about the black hole interiors. So this problem for many years was understood from the point of view of sort of linearized and nonlinear toy models which I'll run through and the main result of this talk which will be it's a joint theorem with with Jonathan Luke from Cambridge in some sense sort of resolves he's still there he's still there on paper and resolves this this issue in some sense okay so I'll I'll um so I say resolves this issue there's still something very important left to be done and that's that would be the end of the talk. Okay so this is my outline so off we go into the interior of black holes and this Strong Kosmic Censorship Conjecture. So the story if you want starts with the Schwarzschild family of solutions as any good story about general relativity should. So Cecil in her talk this morning already introduced the initial value problem for the Einstein vacuum equations the equations Ricci curvature of the Lorentzian format 4 equals 0 in some sense the first non-trivial solution of these equations to be discovered is the celebrated Schwarzschild family. This was discovered actually already in December 1915 and published in in January 1916 so we are really celebrating the centennial of the of the publishing of this of this solution. So what I want you to know about the solution one could certainly give a whole lecture just about the solution but what I want you to know for the purpose of this talk is the following facts all of which are written on this slide and which I'm going to go through. So first of all you can think of this as a solution of the initial value problem and it arises from sort of good initial data in particular asymptotically flat complete initial data the only funny thing about the initial data is that it has two asymptotically flat ends and I've depicted sort of the initial data in this sort of schematic description okay where actually every point here is a sphere okay so this topologically is s2 cross r and this and this are the two asymptotically flat ends okay so it's a solution that arises from regular initial data nothing nothing is wrong with the initial data on the other hand the solution itself is geodesically incomplete okay so in some sense this is the first example of why global existence does not hold for the for the Einstein vacuum equation you already see it in in this solution so the solution is geodesically incomplete okay but at the same time observers at infinity they live forever so how is that possible and what does that mean so you should think that observers at infinity is just the sort of a way of saying you know parametrizing the limit t plus r goes to infinity okay so that limits very important general relativity because that's where gravitational radiation is detected as we found out last February so um so now a sort of limit you can think of it as an ideal boundary of spacetime called future null infinity this is depicted here it has two connected components because as I said the data has two asymptotically flat ends and those sort of that boundary at infinity is itself complete okay so if you normalize time at null infinity then time goes on forever in both the forward and past directions okay at the same time if you ask yourself what is the past of null infinity what are the points in spacetime that can communicate with these far away observers then that past has a non-empty complement and that's what if you learn to sort of read these spacetime diagrams that's what's depicted here so in general when the past of future non-infinity has a non-empty complement we call that region the black hole regions basically so Schwarzschild is also the most basic example of a solution of the Einstein vacuum equations with a black hole region okay so it it so happens that any observer so any time like geodesic that enters the black hole only lives for finite time but all the observers who refuse to enter the black hole they live forever okay so somehow you have geodesic incompleteness but the incompleteness is hidden inside of this black hole region okay so that's sort of the second thing that I want you to take away from from Schwarzschild but then there's a third thing which in some sense is the most interesting from the point of view of this talk what what happens to observers who enter this black hole well I already told you that they only live for finite time but why is that so it turns out that you can picture them as asymptoting to a singular boundary of spacetime at which the curvature blows up okay and this boundary is r equals zero okay and there's something more you can say about this singular boundary than the fact that the curvature blows up so first of all it is spacelike so again that is manifest from this depiction if you know about spacetime diagrams but one can also relate it to the talk of Zag yesterday so in the language of his talk that's the statement that every point in the boundary is non-characteristic okay so that's really sort of equivalently the statement so this is a spacelike singular boundary and moreover not only does the curvature blow up which we're sort of we know from PD theory that curvature blowing up per se is not necessarily fatal the the metric itself blows up in some sense and well the correct way to say that is that the metric is inextensible beyond r equals zero even as a as a merely continuous Lorentzian metric and actually that statement was only recently proven nice paper of Jansbierski so to summarize Schwarzschild it emerges from perfectly fine initial data but the spacetime is not fine it's geodesically incomplete on the other hand faraway observers they live forever and the incompleteness is in the black hole and if you are so silly as to enter the black hole then you only live for finite time and moreover you will be torn apart by infinite tidal deformations and in some sense being torn apart by infinite tidal deformations you should think about as being related to the fact that it's the metric itself that breaks down not just the curvature so it's a very strong singularity and moreover the singularity is spacelike okay which means nearby points sort of on the singularity you know do not communicate with each other or again in the language of zag the points of the singularity are non-characteristic okay so this is Schwarzschild all right but let me already say a big conjecture in general relativity that I'm not going to talk about but is motivated already by Schwarzschild and this is the so-called weak cosmic censorship so when Schwarzschild was first understood geometrically people thought that all these behaviors were bad and pathological and there was a hope that all these behaviors at the end of the day were a result of Schwarzschild being very symmetric and in particular there was a hope that if you perturbed the initial data leading to Schwarzschild then you know spacetime would be geodesically complete you wouldn't have a black hole etc etc okay and it's important to remember that that that hope was spectacularly falsified in a very short seminal paper of Penrose from 1965 when he proved his celebrated incompleteness theorem and a corollary of this theorem is the statement that if you perturbed Schwarzschild's initial data and solve the Einstein vacuum equations you're still geodesically complete okay so so when you take a second look at Schwarzschild then Schwarzschild isn't that bad because at least this incompleteness is hidden in black holes okay so this gives rise to a conjecture known as weak cosmic censorship which says that for generic and I'll get back to this word generic asymptotically flat vacuum initial data you always have a complete null infinity so you should really think of this as the statement that you know very far away observers in the radiation zone they live forever so this is really if you want the global existence conjecture in general relativity which is still compatible with Penrose's incompleteness theorem so why generic why not for all initial data well actually the our only understanding of this conjecture comes from a toy model studied back in the 90s by Dimitri Stalulu namely the spherically symmetric Einstein scalar field system and he proved the analog of this conjecture restricted the spherical symmetry but he also at the same time gave examples of space times for which complete for which future null infinity is not complete so such space times are said to possess a naked singularity so he proved that they were non-genetic but he also proved that they exist okay so this is something to keep in mind I'm actually giving you this conjecture also so that the name of the main conjecture I'm going to talk about makes more sense but anyway that's it's a nice conjecture that we should all know if we want to study relativity all right back to Schwarzschild well Schwarzschild it turns out it does not come alone as a solution of the Einstein vacuum equations it's embedded in a larger two-parameter family of solutions which are much more subtle and were discovered much much later and are known as the Kerr family of solutions so if I could spend the whole lecture on Schwarzschild I could spend maybe a week of lectures on the geometry of the Kerr solution I don't have time for that and you certainly don't want to listen to that so let me just tell you what we need to know about the Kerr solution for the purpose of this talk so first of all just like Schwarzschild these Kerr solutions are again judicically incomplete okay and they again have a non-trivial black hole region in fact qualitatively speaking the initial data looks much like Schwarzschild it's sitting on the same topology it's again asymptotically flat with two ends and again there's a future null infinity with two connected components again future null infinity is complete so far away observers live forever this is not a counter example to weak cosmic censorship all right but if you look at the past of future null infinity okay that's this region here and this region here that has a non-trivial complement in the spacetime the black hole region okay so all that is just like in Schwarzschild but now there's a difference when we look at the interior of the black hole region turns out that the the interior of the black hole region is not bounded by a sort of a space-like singular boundary where all observers approaching are torn apart on the contrary the the interior of the black hole region or at least the interior of the region which is uniquely determined by initial data is bounded by a null boundary on which the solution is everywhere regular so moreover that means that you can smoothly extend the solution beyond this boundary okay and we call the boundary a cushy horizon okay so what's what's happening here okay you see we can extend the solution beyond this boundary but these extensions will no longer be globally hyperbolic that's to say they are no longer uniquely determined by initial dot so here's a situation that does not happen in the model problems that we heard about in the talk of zog here you see that the the boundary of the cushy development can be everywhere characteristic and moreover nowhere on the boundary does anything blow up okay so this is something very very strange from the point of view of the the model problem that we saw about and it's because you don't necessarily have a quote at first singular time all right and this really has to do with um well the sort of fact that if you want time is relative in general so um so you might say this is much better than Schwarzschild it's much better to not blow up than to blow up right and it's certainly much better from the point of view of this observer here this observer sails past this cushy horizon presumably into some extension we just don't know what the extension is but from the point of view of the theory this situation is actually thought to be worse the reason that it's worse is that here we see a breakdown of determinism of the ability of the theory to predict the future and there's nothing that manifestly says that you have left the validity of the theory there's no blow up nowhere so that's very very strange so in some sense uh the situation in Schwarzschild where everyone is accounted for observers who don't enter the black hole live forever observers who enter the black hole are torn apart this sort of is more satisfying from the point of view of determinism i have a question is there any sense where there an m tilde can be taken to be maximal you have a choice of m tilde well you can try to sort of take a bigger and bigger m tilde but that's certainly not a unique object right i mean you can try to sort of look at extensions which are themselves inextendable in various senses so so there isn't that notion a maximal but but not a maximal i don't know right um so so in fact this behavior is deemed to be so pathological and so sort of worrisome that uh one stance to take is that maybe this is all the fluke maybe it will go away upon perturbation of initial data and this happy thought uh motivated uh Roger plenrose back in 1972 to conjecture the following for generic asymptotically flat initial data for the ancient vacuum equations then the solution spacetime which is determined by initial data so if you want the analog of the darker shaded region here okay cannot be extended as a suitably regular lorenzian manifold so of course here it's clear why you have to say generic the curr solution itself does not satisfy the predicate of this conjecture okay so this this says that in particular curr inside the black hole has to be unstable okay but more generally sort of any generic initial data okay should have the property that the koshi development is inextended so as is written here you can really think of this conjecture as the statement of global uniqueness in general relativity just like the weak cosmic censorship is the statement of global existence okay so in fact those would be much better words for or names for these two conjectures because there's nothing about this conjecture which is stronger than this conjecture they're really two different statements so the only some sense sounds better than existence of course needless to say so the only sense that this this is sort of stronger than this is that the the curr family is a sort of counter example for strong cosmic censorship you know we're a generic whereas it is not for weak cosmic okay but in general these statements are not one is not weaker stronger than the other okay so this is this is the the the conjecture so so far i've i've only motivated this conjecture by philosophy and actually i just came back from a conference on philosophy of science and believe me after attending that conference you don't want your conjectures to be motivated by philosophy uh so it turns out that there's a there's an honest reason to hope that this conjecture might be true and this was also first put forward by penrose and it's the so-called blue shift instability so what he observed is the following so imagine you have two observers observer a and observer b where observer a enters the black hole and observer b does not so these two observers are are depicted here and imagine that observer b sends a light signal to observer a at a finite rate as measured by observer b so every two seconds whatever now remember observer b not entering the black hole means that observer b lives forever okay so observer b sends infinitely many signals over the sort of course of his or her life to observer a other hand observer a reaches the cushy horizon in finite time okay so all these infinite signals observer a sort of receives them in finite time which means that the the frequency okay of the signal as the observer a's time goes to this time volume goes to infinity so it's infinitely shifted to the blue in the electromagnetic spectrum so this sort of geometric optics type instability penrose argued would cause solutions of the wave equation on this background to blow up in some way at the cushy horizon and then you can think of this wave equation this is just the covariant wave equation scalar wave equation on this background as some naive model for the linearized Einstein equations okay so maybe that means that at least in linear theory we see that sort of you have some sort of blow-up of something associated to the cushy horizon okay so this was actually his heuristic argument and this in some sense this was the heuristics behind making this much more ambitious conjunction but actually people took this argument one step further so of course if you look at a linear wave equation on a globally hyperbolic spacetime then you can only blow up at the boundary you cannot blow up inside the spacetime just as a matter of principle on the other hand if if you now take into account the full nonlinear theory you might think that once sort of linear perturbations start getting big then nonlinearities will take over and that would cause the spacetime to blow up before sort of you know the the boundary of the original spacetime that you were perturbing okay that's to say you might expect that you would develop a space-like singularity before being able to reach this sort of null boundary or again to use the terminology of Zag that might make you expect that sort of the boundary should now be non-characteristic okay and singular so um so somehow the working hypothesis that most people sort of subscribe to was that the generic dynamic solutions of the Einstein equation would look causally the causal picture would look like Schwarzschild this is sort of funny because of course the Schwarzschild family is non-generic within the Kerr family but the claim was that if you looked more generally within sort of the so all dynamic solutions then the generic case would be would look like Schwarzschild and this is something that has been discussed in in the physics literature sort of for a very long time and many people have have have written about this so let me isolate this statement as what I'll call very strong cosmic censorship and again because unfortunately strong cosmic censorship is not called the global uniqueness conjecture I cannot call this the strong global uniqueness I have to call very strong okay so very strong cosmic censorship says essentially that that for generic vacuum asymptotically flat initial data the part of the solution spacetime determined uniquely by initial data cannot be extended the salarency and manifold and now I'll tell you exactly in what way okay even with a metric assumed only continuous okay even with a metric assumed only continuous all right that's to say in exactly the same way that Schwarzschild could not be extended and moreover I'll throw in for good measure the statement the singularity that can be naturally thought of a space like so this boundary is non characteristic terminology merlin's act so this is the very strong cosmic censorship and this is in fact the the sort of formulation that was sort of widely believed can one always make this comment that whenever you have a space like singularity you'll have the metric will have no no in fact it's sort of as the paper of zbirsky shows it's a very tricky business to show that a metric cannot be extended even just as a continuous metric exactly because there are no you know point wise invariance that capture that so it's it's tricky and in fact it was zbirsky who first proved that minkowski space is not extendable as a metric with as a lorenzian metric with continuous metric so even that was not known all right so let me give you a little bit of the prehistory of the problem even though some of the prehistory is very very recent as these things go so actually let me start with penrose's heuristic argument it's actually very very easy to show that so I'll draw for good measure so this is this picture of the current metric this is the event horizon boundary of the black hole region this is the black hole region this is non-infinity and this is the koshi horizon it's very easy to show that if you have initial data you can find initial data for the wave equation in the energy class so with finite energy such that the solution here okay so if I look at the hypersurface transverse to the koshi horizon we'll have infinite energy here okay and you can do this exactly by the sort of geometric optics argument in fact there's a proof of that by zbirsky using gaussian beams so that's very easy on the other hand of course we all know even from the stability of minkowski space that when we think of perturbing kerr we're not perturbing in the energy class we're perturbing sort of in some sort of weighted energy class and now you might somehow worry that the the decay that that generates will compete with this sort of blue shift instability effect so actually you can show that the blue shift instability wins and this is a theorem both on sub extremal rise or north stroke which is a poor man's sort of version of kerr but also on on kerr itself in the in the full sub extremal range and essentially the statement is that generic solutions of the wave equation which are localized in fact they can they can decay very very fast to a space like infinity will fail to have finite local energy everywhere on the koshi horizon okay so indeed in linear theory there is yeah there is some truth to what panos was saying okay so um so anyway there are all sorts of other comments that one can make so in particular you can actually relate specifically a lower bound for the sort of tail of a solution of the wave equation on the event horizon to the blow-up of the local l2 norm of of its gradient at the koshi horizon okay so there's something in fact you can you can say like that which is very important for particular for for the future all right so this is the this is the the blue shift effect so it's there but at the same time um it turns out that this blow-up is weak so i told you that the local energy of the solution the generic solution of the wave equation is infinite but it turns out that the amplitude of the solution c itself remains uniformly bounded in the black hole interior all the way up to the koshi horizon and in fact not only is it uniformly bounded it turns out that you can continuously extend it to the to the koshi horizon and thus to some sort of larger region so this was a theorem of uh an fransen and while there are also various sort of extensions and generalizations maybe let me not talk about them here uh so let me just say a few words about the proof of this just to give you an idea uh so just to recall this is all consistent right the generic solution will blow up in sort of h1 lock if you want but will be sort of remain continuous okay so to prove this theorem you can make use of results that tell you everything you want to know about solutions of the wave equation on the exterior of a of a sub-extremal Kerr black hole in particular you know that let's say tangential derivatives of c to the event horizon okay they decay like v to some negative power and the only thing i really need to know about that power is that it's bigger than one that's the only thing i need to know okay so this was uh sort of for sub-extremal Kerr was a theorem of of mine with Rudnianski and Schlapp and Tokrothman so starting with this information and using so-called redshift vector field this type of decay for c propagates it's very easy to show into a little region inside the black hole interior so so that's easy to show and then it turns out that you can do a a nice estimate in the rest of the region using a vector field it's not so difficult to write down it's of this form and the only thing that's funny is the coordinates so for those of you who know about uh sort of standard coordinates in black hole theory these are Eddington Finkelstein like coordinates in the black hole interior okay so this is v equals infinity and this is u equals minus infinity okay so it turns out that you can apply and p again will be greater than one you can apply this as a vector field multiplier to the wave equation and this assumption allows you to bound the initial energy terms okay so then if you think about it uh bounding so what does that mean on a on a hypersurface like that you're bounding something like this dv okay so if you think about this then after further commutations this type of a bound because p is bigger than one allows you to show that the c remains bounded in fact uh extends continuously so this is what she did um okay so uh so that's um honest theorem so now let me make some comments so of course if you naively extrapolate now this linear behavior for the linear wave equation to the Einstein vacuum equations then what would you do you would identify pc with the metric and derivatives of c with the crystallism so i just told you that pc doesn't break down in fact extends continuously but derivatives of c they they blow up here in fact they're not even locally l2 so that would suggest if you could just extrapolate that when you perturb curr initial data okay the cushy horizon survives as in no bifurcate hypersurface and the metric remains close to the curr metric just in l infinity all right uh on the other hand higher derivatives of the metric should be blowing up so that would mean that the boundary is something that one could call a weak null singularity even though for various reasons the name is not so great uh this blow-up is such that you're no longer even a weak solution of the Einstein equations okay but the blow-up is much weaker than in schwarz okay so hence the name um so anyway there was some evidence for this actually which came out of a sort of analysis of some fully non-linear spherical symmetric toy models again there's a big literature on that and i contributed to that uh many years ago on the other hand uh most people did not believe that this extrapolation uh was correct that's to say uh in particular if you believe this original intuition then in the absence of symmetries then the non-linearities of the Einstein equation should just take over once they once the perturbations become large enough and you should get a space like a singularity before okay so the question is which of these two scenarios hold okay so let's leave all this linearized and sort of toy models behind and and go to generic dynamical black hole interiors so if if you're a fan of this scenario i sort of was i admit then the first question you have to ask is can you even just locally construct just a piece of vacuum spacetime which has a null boundary which is singular in in the way that it would have to be by this extrapolation because you know there are no explicit solutions of the vacuum equation that sort of exhibited this type of singularity and this is one of the reasons that many people thought that you wouldn't have that so uh so can you even just locally construct this and this problem was resolved by jonathan luke in a remarkable paper of a few years back and he he constructed such examples by solving a characteristic initial variable so let me sort of draw his theorem so um he considered initial data for the Einstein vacuum equations that were posed on uh if you want on on what would be the future of a sphere okay so this is a sphere it's outgoing an ingoing light cone okay so i'm going to draw these two light cones just like this okay so this is the sphere and these are the two light cones okay so um so how do you prescribe characteristic initial data for the Einstein vacuum equations well actually there's in certain senses it's it's more easy than space like initial data because it's more easy to deal with the constraint equations and it turns out that essentially the free data is given by the shear of this cone and this cone okay plus some information coming from here okay so the shear is in honor of christel luke and kleinerman is typically denoted by a he hat and he bar hat this is the shear of this cone this is so shear just means that the traceless part of the second fundamental form okay so that's really the free data you you basically get to prescribe that um arbitrarily okay and then you're going to try to solve the Einstein vacuum equations in a double no gauge okay that's sort of tailored very nicely to this sort of setup that's to say you're going to construct locally a spacetime which is foliated by ingoing and outgoing null cones okay which are drawn like this okay and in this picture okay this is sort of the these would be those light cones okay and uh i'm going to sort of you can think of these light cones as defining two null coordinate systems okay so my uh so one sort of coordinate system will be v equals constant and the other will be u equals constant okay so this i'll make it v equals zero okay and this if you want is i don't know u equals zero okay so these are constant us and these are constant these so what he says is okay i'm going to choose the initial data okay to be singular as you go here okay and moreover to be singular as you go here all right in a way that would make the crystalline symbols fail to be l2 okay so this is a crystalline symbol it's second fundamental form okay so what's your favorite function which is not an l2 but is an l1 why should it be an l1 i want the metric to be continuous and the metric is an integral of this you should think so my favorite function is what's written there v to the minus one uh log minus v to the minus p for p bigger than one okay so this is this is v equals zero this is uh sort of barely an l1 okay but it's certainly not an l2 okay so this is very singular initial dot okay so you might expect that even if you can prove well positeness for the initial value problem the solution will only exist up to some region like this okay and what jonathan luke proved is that no the solution exists all the way up to v equals zero at least if i restrict to small enough sort of time in this direction that's what he proved so i can't say much about this proof but let me just say a few words which are really geared to to to the experts um so when you write the sort of ishon equations in such a double null coordinate system you have the metric you have sort of christoffel symbols and you have curvature okay where these are written with respect to a sort of a null frame which is tailor made to to to these sort of double null coordinates so anyway i mean there's some notation for the metric components and again this is really for people who know about this otherwise you can read a book for hopefully not more than two minutes so these are examples of christoffel symbols and then uh we also have curvature and what um what jonathan did is the following so first of all it turns out that uh if you look at the expected behavior of some of the curvature components it's just too singular to do anything so a very remarkable thing happens you can renormalize the system you can drop these and you can redefine rho and sigma and you can write again a closed system of equations so the redefinition of rho and sigma essentially you replace rho with the the gauss curvature of the spheres of intersection and you replace sigma with something that looks like this so this is called sigma hat or sigma check rather but this actually has a geometric interpretation that i won't get away to and and now sort of these quantities are less singular so this is actually something that arises from some earlier work of rodianski and luke so what what they actually showed is that if he had is assumed to be somehow if he had is assumed to be an infinity okay then you can um you know you can still sort of close estimates for this renormalized system okay and prove a local well poses okay but here uh he had is much uh less regular so it turns out that yeah yes but it's it's a yes and philosophically yes certainly philosophically yes okay so what what uh what he showed here is that you can prove weighted estimates okay for these quantities where you introduce a weight which sort of uh cancels this singular behavior and you can close estimates uh for these quantities now of course secretly what's going on is there's there's a very subtle null condition for these renormalized quantities that allows you to sort of control things okay so i don't really have uh time to say more uh about this but just sort of remember what's on the board and remember this funny expression here okay so the other thing that maybe is is good to sort of emphasize you can think of this as a low regularity well posed as theorem and when you think of it as such you see that it's much lower than the the sort of best general local well posed in this theorem which is the l2 curvature theorem of serju and uh Jeremy and Rognanski okay and the reason is that here the yeah the crystal full symbols are not in l2 okay so it's really much much more singular on the other hand that singularity is compensated by extra regularity in other quantities okay and if you want this sort of null condition plus this renormalization is what tells you that okay this is consistent and propagated okay so this is what Jonathan did in his really remarkable paper and in fact it gets even better because he showed that well not only can you sort of have one of these singular fronts but you can choose the data so that here also let me read read yeah change u equals 0 to here so this is u equals minus doesn't matter okay you also have a singular front here and you can arrange the data so that you can solve in this whole neighborhood here in all of it okay so you have existence up up to if you want this sort of bifurcate sphere okay so this creates a little piece of spacetime okay such that the spacetime is has a weak null singularity here and here okay all right moreover you can you can extend continuously sort of the metric beyond okay so that was that was Jonathan's work so this is really great this tells you that there's nothing wrong in principle with having weak null singularities but of course it does not tell you that weak null singularities occur inside black hole interiors okay it just says that in principle that it's not inconsistent but so how does one show that weak null singularities occur in in black hole interior well you have to start with some information so of course in linear theory when i talked about Anna's proof that solutions of the linear wave equation remain bounded she could start with the fact that we know that solutions of the linear wave equation they decay polynomially sort of to zero at a sufficiently fast rate now the analog of that statement in non-linear theory is not yet known it's none other than the conjecture that the exterior region of the curved black hole is stable so so for the purpose of this talk i'm going to assume this conjecture to be true okay so then the theorem which is forthcoming and hopefully very soon will be out which is joined with Jonathan Luke says the following if indeed the curve solution is stable in its exterior then the Penrose diagram of curve is globally stable and moreover the sort of solution is extendable beyond okay as a continuous metric just like currents so in particular if the exterior region of current stable then a very strong cosmic censorship is false so let me just say very very briefly just to say something about this proof maybe i'll say it here because it sort of goes better with with what's written here so what what does it mean to assume the stability of curve it means that you can start the problem here that's to say you can start the problem if you want from a bifurcate null hypersurface that would be the event horizon of these dynamic space times and the assumption which is given to you by the stability of curve essentially says that the shear of this cone and also this one but let me always talk about sort of this side okay decays at a suitably fast polynomial rate so something like this okay so in fact all we need is that we have initial data so this initial data is complete so v goes to infinity okay so all we need is that we have initial data which is approaching curve at this rate okay and these rates are not thought to be sharp okay so this is sort of a weaker you need sort of a weaker version of what's going to be true he has to be bigger than one that's all just one so so now again it's it's very easy to show that things propagate to a sort of the analog of an r equals constant space like hypersurface a little bit in the black hole that's very easy you do it with redshift techniques and then what you want to do is you want to apply the analog of this vector field to all these components okay and so the remarkable thing that happens is the following so you can apply these vector fields to all components of this renormalized system and for a large time as you're approaching the Cauchy horizon you think you're essentially showing a global existence result with a null condition but actually this coordinate v is related to sort of local coordinates at the Cauchy horizon let me call local coordinate capital V by the transformation e to the minus alpha v equals let's say minus capital V where alpha is some positive constant so what's remarkable about all this is that if you do this transformation this behavior sort of gets transformed into this behavior with capital V and so these weights mesh with exactly with sort of the weights that come in this theorem and it happens without even thinking about it yeah yeah so here the bigger the p the faster you decay yeah this p makes it less singular remember this p makes this less singular or less i because remember this is blowing up the log okay so so let me just make a comment this theorem is not telling you that the boundary is singular and in fact the boundary will not be singular for all initial data particular core data it's not singular okay this is just telling you that if it's singular it's not too singular on the other hand since we expect that it will be singular generically the estimates have to be compatible with exactly the singularity that supposedly will have okay all right let me just give a few more comments i will not take more than two minutes so one minute okay so let me first give an aside there's a cousin of this problem sort of younger cousin you can add a positive cosmological constant to the Einstein equation and well it's hard to find this solution in a textbook but there is a solution called the Kerr-Desider solution which would be the analog of the Kerr solution in if sort of you add this cosmological constant to the Einstein equation now unfortunately sort of in the regime where we have black holes the cosmological constant is zero so these don't really occur in physics as we understand it but they're a very nice mathematical model and in particular very very recently a week ago peter hints and andros wasi showed the stability of a certain region of this spacetime namely the region bounded between the event and cosmological horizons okay so actually sort of if you look at this Kerr-Desider spacetime in the region beyond the event horizon then essentially adding lambda is not so important and our theorem actually applies so in particular using this and our theorem you can show that the analog of strong cosmic censorship if you add this cosmological constant is unconditionally false so so and we will we will write something about this actually this spacetime has another interesting region namely a cosmologically expanding region and its ongoing work of slu to show the stability of that region so let me finish with what's left to be done very very quickly open problem one will prove the stability of the Kerr exterior once this is proven then indeed very strong cosmic censorship will be falsified as a corollary and open problem two as i said i'm only showing the stability aspect i'm only showing that the koshy horizon is still there so open problem two is to show that for generic initial data the solution is inextendable if you require that the crystal symbols are locally square intubable and the motivation of this so this you can think of as a weaker formulation of strong cosmic censorship it's due to the crystal zulu and the motivation if you want for this is that it tells you that well maybe you can extend to some sort of metric but those metrics are not even weak solutions of the ancient equations because sort of the derivatives of the metric are not square integral so this would be at least some some consolation so corollary of this would be that the crystal zulu formulation of strong cosmic censorship is true in a neighborhood of the kerf family now i warn you to show that a version of strong cosmic censorship is false of course it suffices to show that it's false in the neighborhood of some solution because it's conjecture about generic initial data to show that it's true you really have to show it something about the whole modular space of solutions so a complete proof of this version of strong cosmic censorship appears to be something far away in the future okay sorry to go over a little bit thanks so when are we going to see the paper hopefully hopefully very soon i mean i tell my collaborators not to have babies but they don't listen yes maybe another another question which is you're giving us a criteria on the horizon and that criteria is shifting a little bit so you have a i don't want to say philosophy but you have some sense of what physically would be a more desirable criterion here you have very strong here you have weak singularities but not l2 now you talk about cristobal symbols and their singularity but their el tunas we have we've had a variety of singularities on horizons and just tell us what you feel about well i mean what what so it's not to get into philosophy which i heard a lot about in vienna last weekend but actually your question is in fact so i i i didn't mention but there's another interesting thing about the case where you have positive cosmological constant which is that now you have many parameters in the solution you have the cosmological constant the the rotation parameter in the mass and it turns out that heuristically as you sort of move towards extremality in this in these parameters and you sort of do some heuristics then this suggests that actually the singularity that you would expect on the cushy horizon gets weaker and weaker so in particular you you expect that the closer you are to extremality than the higher sort of lp norm you lp regularity you have for the cristophosomes so in particular if you are sufficiently close then they will be in l2 and and that's really troubling because that tells you that the um cristidulu formulation strong cosmic censorship is probably not true uh if if you have cosmological constant so that could even be an argument that there should not be a cosmological constant people want a philosophical argument uh for sort of why cosmological constant is bad that that could even be used as such but in any case that's that's to say that the the you know unfortunately the answer the final answer is not as clean as we would have liked it to be and uh you know as a result sort of it does open the door to all sorts of speculation what what is the interpretation of this singularity should we you know is it the end of spacetime or is it not and the sort of it's not as definitive as it would have been had very strong cosmic censorship been true i guess some would allow a continuation and others would not allow continuation yeah so the question is sort of what yeah what types of continuation are physically admissible and we we just don't know okay is this something you expected the data that's allowable on the horizon is everything of the form chi had smaller than v minus p yeah and like your hope that that would be all all data just a simple net point like that with the that's the thing i mean we we start we start with this assumption and we solve the but there is thinking of that's coming from uh from uh selective fed data it doesn't nothing now i mean it's sort of whether this came from an asymptotically flawed region is not relevant anymore no i understand for your theorem but i was wondering so basically you expected just the data that's consistent with the asymptotically flat condition is just chi had smaller than v minus p yeah well i mean there are more info i mean there's also i'm i'm suppressing the fact that you're also some sense this should be a curse fear i mean this is a limiting sphere that's to say that your your your solution is approaching current okay but you can think that this is sort of what parameterizes the free data on the horizon okay and what you really need is that the free data is decaying sufficiently fast and it's not you don't need what's thought to be short all that that is the case officially fastest coming from something that's uh that's an asymptote well you have to add more data you can try to add data here of course uh as we all know sort of solving the scattering problem has its own difficulties so one part of it's so slow anyway so yeah they apologize but they you know i am under pressure can you say so we can have discussions uh thanks again thank you


Hello, everyone, welcome to Chrome Dev Summit workshop. My name is Eiji, and I'm a developer advocate at Google in charge of front-end security on the web. This workshop is Gain Security and Powerful Features with Cross-Argent Isolation. And Cross-Argent Isolation has a new browser capability that lets you use Shuddery Buffer and Hypercision Timer securely. In this workshop, you're going to learn recap of how web is built, Spectre and its mitigation on browsers, what is Cross-Argent Isolation, how to deploy Cross-Argent Isolation, challenges, and improvements, and summary. I don't know how other people run their workshop in the Chrome Dev Summit, but this workshop is not like a codelab. Instead, this is going to be a presentation-style session, but have a few demos you can play with so that you can learn how things work by actually adding headers to a demo website. You can feel free to ask questions using the chat on the Google Meet. You can find the chat mark at the bottom right corner of your screen. And I will answer them whenever I find it's good time to do so. It's going to take about an hour, and in case some of you will need to leave early, I will start with a spoiler. If you want to use Shuddery Buffer, now you have two options. One, simplify your website and take all the efforts I will explain in this session to enable Cross-Argent Isolation. The second, continue the status quo and keep it available only on Chrome desktop by registering the Precation Trial, at least until Chrome 103. To learn how you will come to this conclusion, please continue with this workshop until the end. Before we actually dive in in order to make this workshop more fun and entertaining, I prepared some quizzes for you. Please go to menti.com and enter the code, or simply scan this QR code with your phone to enter the quiz website. In this session, I'm going to talk about origin relationships, such as same origin, same site, and cross-origin, cross-site interchangeably. And I would like all of you to understand what they are quickly. There are three questions. Each has four options to select from. You have 20 seconds to answer. But the earlier you select the correct answer, you get more points. It's going to be fun. So let me switch to the quiz page here. And let's see how many of you have already joined the quiz. Yeah, please let me go back. This is a QR code and a website URL. I will wait for another few seconds until you join the quiz. Please come in. OK, let me get started with the first quiz. Quiz number one. Choose one that indicates ETLD plus 1. You have four options to select from. Please pick the right answer from there. You have 2, 1, 0 times up. OK, so many of you picked the second one. OK, so the second one is ycg.github.io. It's actually the right answer. Let me explain y, let me see. So ETLD plus 1, what does that mean? So TLD, as many of you may know, means top level domains. So something like if you look at the domain, there are a few entities divided by dot. And the right most side of the entity is the top level domain, so that's TLD. Meanwhile, public suffix is a kind of registered TLD manually registered TLD. For example, like .co.jp or .github.io, which is not automatically detectable so that the list is manually curated and it's a public repository. And it's on browser so that browser can look up on this public suffix list to determine what is TLD for that domain. So ETLD means effective top level domain, meaning TLD plus public suffix. That's what is ETLD. And ETLD plus 1 means the one more entity plus ETLD, which means that, for example, google.com or ycg.github.io. If you look up on the public suffix list, github.io is there, so which means that github.io is considered effective top level domain. So ycg.github.io is the only answer you could pick from the previous quiz. And one optional hint for the next quiz is ETLD plus 1 represents a site. Let's move on to the next quiz. Are you ready? Quiz two, which one is same site to hps www.google.com? There are four options, google.com, gstatic.com, youtube.com, blog.google, which one is the same site to www.google.com? Time's up. The right answer is number one, google.com. Let's see why. The same site means, like I said, site means ETLD plus 1. So that means if you say hps.www.google.com, only the google.com part represents the site. So as long as the site part are identical, you can say that they are the same site. So hps.google.com is the same site to hps.google.com. So the right answer is the first one, hps.google.com. Then let's move on to the next question. Quiz number three, which one is same origin to hps.google.com? Which one is the same origin? google.com, hps.google.com, images.google.com, 443. Time's up. Is it a little too short? Many of you picked the number three. Yes, that is the right answer. So the trick is this, the same origin. If you say same origin, it means that three things, scheme, host name, and port number, all of them matches. All of them are identical to the other domain. Means that they are the same origin. So I said that the original question is hps.www.google.com. And the other candidates has 443 as a port number. Additionally, but if you look at the URL carefully, the scheme is hps, which means that it's using the port default port number 443. So it's implicitly has the port number 443 that they can be considered same origin. So that is the same origin. And we have leaderboard. Oh, Giorgio, congratulations. You got the best point among all. Congratulations. Let me see. Someone has asked the question. Oh, my voice is too low. Sorry, I didn't prepare any prize. Cherish hearing now. I'm using the MacBook Pro microphone now. OK, sorry about that. Let me move on to the next section. All right. So now your brain should be a bit refreshed, hopefully. Let me get started with a story about why. But before explaining why, we need to recap some basics. OK, in a browser, each tab has one URL that's displayed at the top and represents where the document the user is looking at is. This is the first part. In addition to that, it loads many resources such as images, videos, styles, scripts, fonts, and so on, including those that are hosted at different origins, which are soul parties, meaning cross-sourcing. You can load these resources and capabilities onto your website without setting up the hosting server by yourself.  For example, you can integrate analytics just by loading a single cross-sourcing script. You can display ads, widgets, personalized videos, and maps using cross-sourcing iframes. You can integrate soul party identity and payment solutions by using cross-sourcing pop-up windows. It shouldn't be an exaggeration to say cross-sourcing integrations is what makes the web today. But why can you say that it's safe to put resources from different origins onto your website? What if a malicious website embeds a personalized widget and steal your cookie? Why can't that happen? Of course, there are many known vulnerabilities and attacks such as cross-site scripting, C-surf, cross-site request for Jolly, click jacking, cross-size leaks, and so on and so on. There are so many vulnerabilities, but as long as you make the website vulnerability-free, the browser keeps your resources safe. That's what we call same origin policy. The browser manages interactions between origins so cross-sourcing scripts can never go beyond the border of origins. For example, you provide a video streaming service. Soul Party websites can embed it and because it's personalized, their customers can watch it there or later on your website by marking it as watch later. This is very typical. The embed is done by using iframe, but a malicious website trying to steal a cookie from your iframe will not succeed because traversing the dump tree across cross-sourcing iframe is restricted by the browser at some point. There's only minimum information available to the parent of the iframe. A similar example applies to pop-up windows. The browser keeps the boundary between cross-sourcing resources firmly. That's what the same origin policy does. However, the discovery of Spectre announced in 2018 changed everything. It's a catastrophic threat to the web that enables a malicious website to even strap cross-sourcing contents by reading their memory despite the same origin policy. Spectre exploits CPU speculative execution and browser's high-precision timer to guess the cross-sourcing contents. Because of the nature of cross-sourcing integration, if a malicious website gets your resources run in the same renderer process and traps your users there, your customers could be a victim. To mitigate the risk that was introduced by Spectre, browser vendors decided to disable some features such as shared or a buffer, and once that relies on high-precision timer to reduce the efficiency of the attack. With that, immediate threat of Spectre was mitigated, but later it's proved that the solution wasn't perfect because it's just a matter of efficiency. A better way of mitigating the risk of Spectre was to isolate the memory space part origin. That's why Chrome decided to introduce a new architecture called Site Isolation. Site Isolation makes the browser processes run part sites as much as possible rather than tabs. Because Spectre's impact is within the same process, this reduces the risk of Spectre-related attacks significantly and could revive the features such as shared or a buffer and high-precision timer that were disabled because of Spectre. Ever since Site Isolation was enabled on Chrome, it has been keeping the web on Chrome desktop secure while enabling the powerful features. As I said, changing the browser architecture is more effective way to protect websites, but the good news is you can keep your website safer by following the standard practices as well, even if you're running a browser that doesn't have Site Isolation architecture. Since this topic is out of scope for today's workshop, I encourage you all to watch the Google IEO video about web security. My colleague Camille and I run this year, but the quick gist is here. The first, control cross-origin embeds of resources with cross-origin resource policy. Second, control cross-origin embeds of iframes with X-Frame options or CSP-Frame ancestors. Number three, control communication between cross-origin windows with cross-origin opener policy. Number four, prevent malicious mime sniffing of resources with X-Content type options, no sniff. So yeah, there's a request. You paste a link there in the chat, but it's a little bit difficult right now for me to do so, but I will, this video will be recorded and will be published so you can re-watch this session, I think. So please try find the video later. Okay, what is cross-origin isolation?  Site isolation looks like a good protection, but it depends on a specific browser architecture. Though Firefox is also trying to follow the same route, websites shouldn't rely on the browser's architecture. There should be a standardized mechanism to declare that this is an isolated, safe environment. That's where cross-origin isolation comes in. Earlier, I explained that there are HP headers to keep your origin isolated from others. It's considered safe. Then, yeah, thank you. Someone pasted a link in the chat of my YouTube video. By the way, thank you, Giorgio. Sorry, come back to the original topic. Then why not enforcing your website, isolate it from others so that the browser can safely enable powerful features such as shelter or buffer? That's the basic idea of cross-origin isolation. Note that Chrome has already shifted to require cross-origin isolation, even though we have site isolation, in order to use shelter or buffer to align the behavior with other browsers since Chrome 92. That's why we asked everyone to apply for cross-origin isolation. Then, now, here's how to enable cross-origin isolation. Two headers are required. One is co-app, cross-origin embedded policy, require corp, and the other is coop, cross-origin opener policy, same origin. Let me explain further. Cross-origin embedded policy, require corp, instruct the browser to load only the resources that opt in to be loaded with course, cross-origin resource sharing, or corp, cross-origin resource policy. There are so many abbreviations, so please catch up with me, follow me there, that shorthand acronyms. This ensures your website will not put resources loaded cross-origin in danger. Cross-origin opener policy, same origin, instruct the browser to restrict the communication with the window that opened this window or is opened by this window, so mutual communication. This ensures that they will not share its process cross-origin to protect itself from specter-related attacks. By combining coop and co-app, cross-origin opener policy and cross-origin embedded policy headers, you can declare that the webpage is cross-origin isolated and shared array buffer and high precision timers are enabled. And now, it's an exercise time. Let's try how it works using a demo site. Please open force-party-test.glitch.me and try enabling cross-origin embedded policy and cross-origin opener policy to enable cross-origin isolation. Okay, let me try to force-party-test.glitch.me so you can easily open this page. Hopefully, that's hand-pipes your is, your is collect. So if you go to the demo page, you will see something like this. Let me refresh just in case. So what you will see is that at the bottom, you will see that cross-origin isolated is disabled, right? And at the second section, you see that set various headers for the cross-origin image where there's an image circle with a check mark is displayed here. Below that is an iFrame. Within the box is an iFrame rendered from the third-party domain which is sort-party-test.glitch.me. It's obviously sort-party-origin. And finally, there's the section that explains the pop-up window. So by pressing this button, it opens a pop-up window. It's cross-origin. But if you click on this send a post-message button, you can see that the other window shows an alert, which means that the post-message message was delivered to the other window. So you could show the alert, okay? Now, let's go back to the header of this page and find the cross-origin embedder policy line here and change it to require corp. Now, let me open the DevTools first. This is hard to see. Up, enlarge the text and change corp to require corp. And let's see what happens. All right, successfully the page is reloaded. And if you look at the network panel and see the top-level document, you will see the bunch of headers here. And if you see the response header, there's some message, I will get to it later. But response header says that it's sending, sorry, it's sending cross-origin embedder policy header. It's cached, sorry. Here, you can see that there's a cross-origin embedder policy require corp with report, reporting API at the end, but I will get to it later in this session. So this is cross-origin embedder policy header attached to this document. And what has changed?  It's blocked, why is that? That is because we enabled cross-origin embedder policy, but we didn't get the sorparity resources opted into cross-origin resource policy. So it's being there being blocked. We will fix that later. Now, let's now change the cross-origin opener policy to same origin. And obviously the background color has now changed. And if you look at the DevTools Network panel, there's also one change that you see that cross-origin opener policy is added to the header. So both corp and corp headers are added to this page. That's why this page turned into cross-origin isolated state. Of course, this background color effect is what I made manually. So that is not happening to your website, of course. And as soon as I added cross-origin opener policy, same origin, that means that the communication between this window and the window open from it or the other window will be blocked. Which means that by opening a pop-up, let's try send a post message. And if you look at the other window, no other is shown, which means that the post message has failed. If you read this text here, it says a window is in a different browsing context, which means that it has separate processes between this window and the other window. That's why we cannot communicate each other. These windows cannot communicate each other. All right, let's go back to the slide and continue the session. Let's move on to the next step. Let's say you want to load cross-origin resources. We've seen that the image and the iframe were blocked. In that case, as I said, you will need to enable cross-origin resource sharing course or cross-origin resource policy to those resources. I'm not going to cover cross-origin resource sharing since it's old enough and we don't have much time today. Meanwhile, what corp cross-origin resource policy does is to instruct the browser to restrict the origin, the resource itself is being loaded too. By sending corp cross-origin, the resource opts in to being loaded from any other origins. For iframes, in addition to corp header, you will need to enable corp cross-origin embedded policy require corp as you did for the parent document. This makes sense because they should all declare the loaded resources are opted in. If it's nested, you will need to apply them recursively. And if you want to enable cross-origin isolation within the iframe, you will need to append allow equals cross-origin isolated attribute as well. And now let's go back to the demo site and try again. So first thing you should do is to look at the image section and let's use cores, let's try cores first. So the upper one, cross-origin resource sharing to anonymous and re-load the image and the image is displayed. Why? Because there are two things happening. One is that if you inspect the image, you can see that image HTML tag has cross-origin equals anonymous, which means that when requesting the image to the server, this request will send as cores cross-origin resource sharing. And if the server accepts the cross-origin sharing request, it will respond. So there are two things needed. So what if I choose use credentials? Anonymous means that the request will be sent without cookies, but use credentials will send a request along with cookie. So that's the difference. Okay, let's put it back and try another one, cross-origin resource policy now. Let's pick cross-origin and re-load. And the image is displayed once again. And if you inspect the image and you will see that cross-origin resource policy is properly sent, responded from the server, right? That's why it is accepted and rather decided to load the image. Note that the header is visible in the DevTools, which means that the resource itself is actually transmitted from server to the browser. It's a browser which decides whether it will be blocked or displayed even though it receives it, right? So the network process decides that, whether it should be blocked or displayed. And only when it's accepted, it is passed to render a process so that browser renders it. Okay, move on to the next section, iframe. For iframe, we will need two things. Yeah, so first thing is to obviously cross-origin resource policy need to be cross-origin, right? And re-load the iframe, still blocks the iframe. What was needed? Cross-origin embedded policy to require a corp. And re-load and boiler. It's displayed now, okay? So iframe requires two things. Cross-origin resource, policy cross-origin and cross-origin embedded policy require corp. And if this iframe document has recursive iframe, it should, the same thing should recursively happen. So they should have corp, cross-origin and require corp. And if you want to make this iframe document to be cross-origin isolated, you will have to append allow cross-origin isolated to enable cross-origin isolation within the iframe. So if you look at the iframe HTML, I have automated it, but by adding allow equal cross-origin isolated, you can enable cross-origin isolation within the iframe. Okay, let's go back to the slide. Now, we learned how things work in theory, but how would we practically enable cross-origin isolation? Before moving forward, I would like to introduce you to the reporting API. The reporting API is a foundational feature of front-end observability, and it's available to corp and corp as well, cross-origin open-up policy and cross-origin embedder policy as well. Usage is quite simple. You define endpoint name and its URL and assign the endpoint to applicable headers. This way, whenever corp or corp encounters a violation, the browser will automatically send reports to the endpoint. Violation as in images or any resources being blocked or the communication is blocked, things like that. We'll be reported. Building your own reporting endpoint is not so easy task to do. There are a few existing solutions, pet solutions such as reporturly.com and urlyports.com. And then there are an open source solution my colleague has built called reporting API for other which can be integrated with open telemetry and open source report collector. So you can connect it with your favorite monitoring tools such as Google Cloud Monitoring or open source monitoring tool called Prometheus and so on. The reporting API is nice, but debugging it is a bit of a pain. We recently added reporting API support to the Chrome DevTools. It might be only canary or dev still. So in case you're now using Chrome stable, you might not be able to try it today, but it's coming there. You can use it by enabling experimental feature in the DevTools configuration. While reporting API is convenient to determine the violations in production environment, Chrome DevTools allow you to debug locally too. Whenever there are issues on your page, the red flag indicates issues. Clicking it opens the issues panel and you can learn more things including how to fix. With that in mind, here's the steps we recommend developers to take. First, define the reporting endpoint by sending reporting and the points header. And next, set coop and quip headers, but with report only mode. Report only mode allows you to receive reports without actually enabling the feature so that you can easily detect where in your website is violating the restrictions. Large website tends to load so many resources that sometimes even the developer don't know what to expect. Run this in production environment gives you a chance to collect a list of resources to fix without actually breaking anything. I think the report only mode is also available on CSP content security policy as well. So some of you might be already familiar with it. Once you have the list apply course or corp, cross-origin resource sharing or cross-origin resource policy, as I said, if there are iframes apply them and quip recursively as well. And whenever you think it's ready, remove the report only mode and finally enable cross-origin isolation. You can check if cross-origin isolation is actually enabled by checking self.cross-origin isolated. It's a simple thing, but you can use it to check whether you can use shared or a buffer or not. I went really quickly on this section, but the same step is described in the URL on the slide. So you can just look back at that page. Okay, now let's try on the demo site and how those things work. Okay, let me reset what we have done first. And the first thing I would like you to do is to click on the link at the top. This will open a reporting end point website, demo website. I have quickly created it. So it will receive whenever there's a violation on the demo site, it will be delivered to this page in real time using WebSocket. So, and it's tied to your session. So you will only see your own violations, okay? And next thing I want you to do is to click on the configuration button. If you're running Chrome, better, I don't know if better can use this yet. If you are using Chrome Dev or Chrome Canary, just in case you don't know Chrome, better Chrome Canary, Chrome Dev are all alternative version of Chrome that are predated. I mean, earlier, more advanced version of Chrome that has the cutting edge features. Okay, Chrome Canary is like updated daily. So every day you get a new Chrome, new version of Chrome and it's yellow. Hope some of you may find it's useful information. So by clicking this toggle, toggle the right word and experiments. And if you go down, you will find a section that says enable reporting API. So check it and reload the DevTools. And now if you go to application panel and go down a little bit, you will see that there's a reporting API section here. Okay, then now please click on report only. So all the headers sent from this page will have report only mode. Let me check with the network panel. If you go to the inspector document, as you can see, the cross-origin embedded policy has report only appended. Also cross-origin open-up policy has report only mode appended. That's why the background color turned to white because it's sending reports, violations, but will not enforce the blocking or communication blocking, right? And the image is successfully displayed here. But this means that there are some issues, obviously. And that's why you see these issues appeared on the reporting end-of-point server. Let's try opening a pop-up and see what happens by looking at this reporting API inspector. Let's see what happens. Open a pop-up. Now you should have seen that there's one more entry added to this reporting API list, report list. And the status has quickly changed to success. But let me try once again. And it starts with queued. And it will be sent in a moment to this other end-of-point server because browser queues any reports and send in batch, kind of bundling different reports and send in a few minutes. So it's batched to send the reporting end-of-point server. Let's see when it will be sent. It's still being queued. It's going to be transmitted in momentarily. Yeah, it's sent and see that it's added at the top, right? So this is what reporting API does. Okay. And also I would like to point out that there are things you can observe without if you are debugging locally without reporting API. Let me remove the report only mode and enable this state. This is the state that you wouldn't expect in the production environment, but you can try it on the locally and see how you can debug this. And if you look at the top of the DevTools, you can see that there's a red flag appearing here. Clicking it will show you that issues that have occurred to this page. And here's cross origin resource policy violation. So despite this page is being blocking the resources with require corp resources without opting using cores or corp will be blocked. And this DevTools issue panel kindly tells you what to do to fix it, right? It's a convenient thing. And also you can find in the network panel, let me reload and if you go to, sorry, not this one. If you go to the blocked entry, you can find here similar guidance how to fix this issue, why this is blocked. You can find the reason why this is blocked. It's kind of, right? So this is how you can debug this cross origin isolation using Chrome and DevTools. Let me go back to the slide and let's continue. All right, so far we've been discussing how to enable cross origin isolation, but they are mostly assuming everything is under your control. From here, let me talk about some common problems and challenges you will likely encounter and discuss what are recommended work allowance. The biggest obvious issue for you is that applying cores or corp on the store party resources isn't that easy. Depending on the website, there are so many resources including ads, widgets, CDNs, and so on to apply the changes, right? Asking all of them to make such changes takes a huge effort and time. In fact, Google ads decided not to adopt corp because even if they do, ads are served from another origin resources, sorry, another cross origin resources, which will not likely easily changeable. The second issue is cross origin opener policy, same origin, which breaks cross origin popup integrations which are typically required by all of or payment integrations. This is a known problem. That environment, both websites cannot call post message and will not function, which is not good. To solve these challenges, we are working on three things. First is corp credential less, credential less mode. The second is anonymous iframe. The third is cross origin opener policy, same origin, allow popups plus quip. Let me explain one by one. For credential less, which that relaxes the restriction from required corp. I said cross origin embedded policy restricts resources to load, restricts resources to load because cross origin isolation puts loaded resources in danger. However, the resources that will be at risk contain sensitive information, sorry, however the resources that will be at risk contain sensitive information and they are not usually public, right? Let me bring it back. You don't want to put resources that have sensitive information to be in danger. Then how about sending requests without credentials such as cookies, then this will only load publicly available resources and we can consider it won't put sensitive information in danger, any sensitive information in danger, right? That is the idea of credential less. So credential less is already available in Chrome 96, which means Chrome 96, if I remember correctly is currently rolling out now, today or tomorrow for you, I guess. So it will be available for you too soon. And the second solution is anonymous iframe. That concept is the same as credential less. It won't send credentials, so it's safe to load. However, the implementation of anonymous iframe is not yet available anywhere even on Chrome yet. We are working on it. And the third solution is about the cross origin window communication. The intention of blocking the communication is to protect the origin from being opened by a malicious website and steal information using Spectre. Then what about allowing communication only when the window is opened by itself, not the other way around? This is why we are working on cross origin opener policy could same origin allow popups, popups plus web. It's a long name. Same origin allow popups plus web. This is a special mode to enable cross origin isolation. Details are still to be determined and not yet available on any browsers yet. But we are actively working on it. So there are the three solutions from standardization perspective. While browser vendors are working on them, many web developers are still struggling to continue using shadowy buffer. We are aware of that. That's why Chrome left an option to continue using shadowy buffer by adopting to deprecation trial. Some of you may have heard a word origin trial. Origin trial is a way to test a new web platform feature before it is shipped by registering your origin. Deprecation trial is similar concept but opposite to it. It's a way to continue using deprecated features after it is disabled by registering your origin. You can register for deprecation trial to continue using shadowy buffer until at least Chrome 103. But unless we have all three new features available on Chrome, we will not terminate the deprecation trial. So you can continue using shadowy buffer without adopting to cross origin isolation. Okay, so that is all I have prepared for this workshop. Thank you all for joining until now. And if you have any questions now is a good time to ask on the chat if you want. Meanwhile, let me summarize what I have talked. Once again, if you want to use shadowy buffer, now you have two options. One is simplify your website and take all the efforts to enable cross origin isolation. So if you have so many resources loaded from different cross origins, it may be hard for you to adopt to cross origin isolation. In that case, you might wanna remove some of them or maybe put in some other pages or so to simplify your website, but you can enable cross origin isolation. The second option is continue the status quo and keep it available only on Chrome desktop by registering deprecation trial until Chrome 103. So my recommendation is just don't bother continue using Chrome desktop if it's okay for you. But if you want to enable cross origin isolation and the use shadowy buffer also on Firefox and soon on Safari, I would definitely recommend you to adopt to cross origin isolation by removing many parts. It may be hard, but that should allow you to make it work across different browsers, okay? All right, let me check what kind of questions you have. Very complex, yes it is. I know I had so many times. So I took a long time to understand all of this. This is one of the most complex topic and we are aiming to make this more simple in the future, but now is a complex transition time. Yeah, learn friendly and easier to remember all these headers. Yes, the presentation. Yes, I think that we are planning to present share the presentation. I will check, yes. Unless you have any other questions, there's the feedback form. Yeah, Rohit added the link to the chat goo.google.cds2121-feedback is a URL for the feedback form. Yes, okay. So thank you for joining me for about one hour. Hope you enjoyed the session.