Pencilvester's latest activity
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Pencilvester replied to the thread Undergrad Convention for writing $\binom{1}{1}$ tensors in matrix form?.I’ve maintained this visual representation as well ever since learning about it in MTW! I can always visualize a vector as a 1-dimension... -
Pencilvester reacted to pervect's post in the thread Undergrad Convention for writing $\binom{1}{1}$ tensors in matrix form? with
Like.
I don't know if this is standard, but I think of a vector, in tensor notation written as ##u^a## as a column vector in matrix notion... -
Pencilvester reacted to A.T.'s post in the thread High School Why is the constant speed of light so unique? with Like.
I find this comparison confusing: - For sound you talk about "moving relative to the wave". (Whatever that means) - For light you talk...
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Pencilvester replied to the thread High School Why is the constant speed of light so unique?.I was never disagreeing with the main point you were trying to make; I was only pointing out the minor mistake in your statement about...
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Pencilvester reacted to PeroK's post in the thread High School Why is the constant speed of light so unique? with Like.
In what way had that point not already been made (several times) by previous posters? @Pencilvester is not the OP!
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Pencilvester replied to the thread High School Why is the constant speed of light so unique?.This depends on the details of a given scenario and is not true in general, no? In the case of your extreme example, I could specify...
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Pencilvester reacted to PAllen's post in the thread Undergrad 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...
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Pencilvester replied to the thread Undergrad 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 Undergrad 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 Undergrad 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 Undergrad 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 Undergrad 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 Undergrad 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 Undergrad 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 Undergrad 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...