Dale's latest activity
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Dale reacted to PeterDonis's post in the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation? with
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Not a vacuum spacetime, of course. But you might be able to by patching together regions with appropriate stress-energy tensors. I think... -
Dale replied to the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation?.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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Dale reacted to PeterDonis's post in the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
Yes, it does! That was my point in post #15. Maximally extended Schwarzschild spacetime, which is a solution that meets the requirements...
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Dale replied to the thread Undergrad The rocket equation, one more time.You can choose whichever convention you like. You just have to be careful to be clear about the convention you use and be careful to...
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Dale reacted to SiennaTheGr8's post in the thread Undergrad Question about special relativity and magnetism with Like.
I think it's worth mentioning that this statement isn't true. The "electricity + length-contraction = magnetism" concept works for some...
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Dale replied to the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation?.Agreed. Such manifolds are not excluded a priori. And since the result of the theorem does not contain such solutions, the conclusion is...
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Dale reacted to PeterDonis's post in the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
No. The areal radius ##r## is an invariant. Picking it as one of the coordinates helps in making the proof of Birkhoff's Theorem look...
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Dale replied to the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation?.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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Dale replied to the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation?.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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Dale replied to the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation?.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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Dale reacted to Pencilvester's post in the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
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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Dale replied to the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation?.I agree. You would have to use at least two separate charts to cover that spacetime.
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Dale replied to the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation?.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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Dale reacted to Pencilvester's post in the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation? with Like.
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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Dale replied to the thread Undergrad Question about special relativity and magnetism.Yes, that is the case. I think you misunderstood the videos, but you correctly understood the physics. The fact that the wire is...