Pencilvester's latest activity
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Pencilvester reacted to PAllen's post in the thread I Is using r as a coordinate in Birkhoff's theorem a limitation? with
Like.
I don't know if I can track it down from a long ago posts of mine, but I discussed a paper by a mathematician specializing GR that... -
Pencilvester replied to the thread I Is using r as a coordinate in Birkhoff's theorem a limitation?.I did not know this! This is very helpful, thank you!
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Pencilvester reacted to PeterDonis's post in the thread I Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
Not a vacuum spacetime, of course. But you might be able to by patching together regions with appropriate stress-energy tensors. I think...
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Pencilvester reacted to Dale's post in the thread I Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
Oh, yes, that is true. I wonder if you could construct an oscillating spacetime like the OP described. I can’t imagine the boundary...
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Pencilvester reacted to PeterDonis's post in the thread I Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
That's correct. There are. One of them is...Schwarzschild spacetime! As I already pointed out in post #15. You are misunderstanding...
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Pencilvester replied to the thread I Is using r as a coordinate in Birkhoff's theorem a limitation?.So, to make sure I'm understanding: any and all statements that can be made about the behavior of the invariant ##r := C / 2 \pi##...
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Pencilvester reacted to PeterDonis's post in the thread I Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
Yes, that's true, you can--for example, maximally extended Schwarzschild spacetime, with black hole and white hole singularities. Nor...
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Pencilvester reacted to Dale's post in the thread I Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
In principle, you should be able to have a manifold with two distinct ##r=0## loci. Consider a sphere, latitude lines are submanifolds...
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Pencilvester reacted to Dale's post in the thread I Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
I think it is proven by Birkhoff’s theorem. Birkhoff’s theorem shows that the spherical vacuum metric is unique. If the metric you...
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Pencilvester replied to the thread I Is using r as a coordinate in Birkhoff's theorem a limitation?.I personally don’t doubt this either, but has this been proven anywhere? If so, I’d be interested to see the way or ways this can be...
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Pencilvester reacted to Dale's post in the thread I Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
I think you are correct that such a manifold is excluded from Birkhoff’s theorem. However, I think it is not a problem with the theorem...
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Pencilvester reacted to Dale's post in the thread I Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
So you are thinking of manifolds where spacetime is foliated as a family of concentric spheres. But the size of those spheres, for...
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Pencilvester replied to the thread I Is using r as a coordinate in Birkhoff's theorem a limitation?.Right, so doesn’t making ##r## a coordinate that ought to cover the spacetime restrict the number of possible spherically symmetric...
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Pencilvester posted the thread I Is using r as a coordinate in Birkhoff's theorem a limitation? in Special and General Relativity.In Birkhoff’s theorem, doesn’t assuming we can use r (defined as circumference divided by ## 2 \pi ## for any given sphere) as a...
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Pencilvester replied to the thread I Convention for writing $\binom{1}{1}$ tensors in matrix form?.A matrix (specifically a square matrix) is a decent way to express all of the components of a (1, 1) tensor. The problem is that the...