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How does GR handle metric transition for a spherical mass shell?

by Q-reeus
Tags: handle, mass, metric, shell, spherical, transition
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George Jones
Feb25-12, 08:59 AM
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I am looking for a new post, written in succinct scientific style (without a lot commentary), of the form

"For a matter distribution given by ..., calculate ..."
Feb25-12, 10:23 AM
PF Gold
P: 706
Here's an idea for a non-stationary matter distribution:

Assume you have 5000 particles, originating from an event (t=0,x=0) and each is assigned a random x and y rapidity between -3 and 3, traveling away from each other in the xy-plane. Assume that these particles move with constant velocity until time t=1.

At time t=1, the particles spontaneously develop mass. Given one of the particles, calculate the force on this particle resulting from the other 4999 particles.

(The proper-time/coordinate-time of the spontaneous development of mass, and the delay before that mass is detected, would need to be more fully described to answer the question.)
Feb25-12, 02:15 PM
P: 16,967
Quote Quote by George Jones View Post
I'm having trouble tracing this back. What, precisely (and succinctly), is the matter distribution in question.
The details are a little fuzzy, but if I recall correctly Q-reeus was claiming that GR was not self consistent because of the transition from the Schwarzschild metric outside a solid shell to the flat metric inside the solid shell.

Somehow the discussion became focused on the space-space components of the (Ricci) curvature tensor and the space-space components of the stress-energy tensor. Q-reeus though you could neglect the space-space components of the stress-energy tensor simply because the time-time component was larger (which somehow led to a contradiction, though I don't remember how).

So I was going to calculate the metric for a finite-thickness solid shell and show that the space-space components of the stress-energy tensor could not be neglected and that accounting for them resolved the supposed contradictions.
Feb25-12, 06:35 PM
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eq (1)











We can add 6.2.3 and 6.2.4 together to get







Feb26-12, 01:03 AM
P: 1,115
Quote Quote by pervect View Post
At the risk of hijacking the thread (which seems hopelessly confused anyway),...
Feel free to 'hijack' this confused thread, which evidently has kicked back into life, and hopefully end the confusion.
Won't comment on the specifics of your photon gas inside a containing shell model, other than to say that there shell self-gravitation as contribution to it's own stress seems to be, understandably, an entirely absent factor. In my scenario, it is the only contribution. If you go back to #1 hopefully my problem statement is made clear enough, and basically what DaleSpam said in #201 sums it up. Again, the specific model settled on was in #17, but that can be obviously generalized.
I walked away from this thread owing to a general failure to get agreement on being able to apply differential length, radial (dr) vs azimuthal (rdΩ), in coordinate measure, as suggested by the standard Schwarzschild coordinates. As expressed in earlier entries, I accept boundary matching from exterior to interior regions is always possible mathematically. Whether that math is properly based on a physical principle (and I was genuinely shocked when it was claimed shell stresses for an entirely self-gravitating shell would do that trick) is another matter!

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