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Oct20-11, 01:48 PM
P: 1,115
Quote Quote by PeterDonis View Post
Ok, that makes it clearer where you're coming from.
Seriously, you didn't get that till now? How about entry #1! Or my posts over there in the blackhole thread which lead to this one. Now come on.
If you doubt the EFE, then the whole discussion in this thread is pretty much useless, because everything everybody else has been saying assumes the EFE is valid.
Last bit obviously true but at the same time everyone here has understood my sceptical stance. The challenge, and my opinions were clearly set out to all you GR buffs from the start. If you feel an explicit and definitive resolution has been given, I'd love a recap because must have missed it.
The puff of air makes the interior region not vacuum; it has a non-zero stress-energy tensor. If the pressure of the air is enough to change the stresses in the shell, then its stress-energy tensor certainly can't be neglected; and a non-vacuum interior region changes the entire problem, because the spacetime in the interior region is no longer flat. Now you're talking about something more like a static model of a planet or a star, just with a weird density profile. (Though again, the density profile can't be that weird, because if the puff of air has enough pressure to significantly affect stresses in the shell, and the air is non-relativistic, then its pressure has to be much less than its energy density, so the energy density of the "air" would be pretty large.) We'll see more specifics when DaleSpam runs the numbers, but these considerations strongly suggest to me that what you have proposed does not have any significant bearing on the original shell problem, where the interior region is vacuum and spacetime there is flat.)
It was evidently all about contrasting vanishingly small self-gravity contribution to shell stress, with what a tiny mass of air would greatly overwhelm - a mass in turn many orders of magnitude less than that of the 8 ton shell. True I didn't run specific figures because seemed quite evident there was no need given the scenario. One gets a pretty good feel for orders of magnitude with that kind of thing (but perfectly happy to put figures to it if challenged to do so). And that bit of air would matter one hoot re non-flat interior spacetime? But it's ok I think I get what's going on and why. Kind of sad but guess this is the end of your participation. So be it - but thanks anyway.

One last thing though. I think it important to know the nature of contribution to metric that in particular uniaxial stress (being the extreme of stress anisotropy), or biaxial if you like, in some element of stressed matter makes. For instance, element having uniaxial stress axis along polar axis - how different are the radial and tangent SC's generated compared to equivalent element of unstressed mass. Would be fascinating to know that, given it's ability to solve the shell issue. You may not wish to bother with a personal contribution, but pointing to a good resource explaining it in a way a layman can grasp would be appreciated. Cheers.