All Questions
12
questions
3
votes
0
answers
88
views
Intuition for the interior Killing vector fields in Schwarzschild?
The Schwarzschild metric represents a stationary (and static), spherically-symmetric, spacetime. These characteristics are manifested by the four Killing vector fields: one for time translation and ...
- 1,290
1
vote
0
answers
62
views
Confused about spherically symmetric spacetimes
I'm following Schutz's General Relativity book and I am confused about his description and derivations of a spherically symmetric spacetime. I searched online and found that using Killing vectors is a ...
- 151
2
votes
0
answers
82
views
Killing Tensors: What quantities do they preserve?
It is known that coordinate transformation generated by Killing vectors (KV) preserve the metric components, i.e. it generates an isometry transformation. Are there similar geometrical quantities that ...
- 1,752
2
votes
2
answers
288
views
Topology in cosmology
Usually in cosmology, we make the hypothesis that the universe is isotropic.
Which conditions does this hypothesis impose on the topology of the universe? Does it fix completely the topology? Are all ...
- 1,335
1
vote
2
answers
736
views
Non-static spherical symmetry spacetime
The Schwarzschild solution is a static spherically symmetric metric. But I wanted to know that how would the space-time interval look in a Non-Static case. I tried to work it out and got
$$ds²= Bdt² -...
- 1,490
4
votes
1
answer
391
views
Prove isometry preserving excision is Killing-like?
(If you think thia is e.g. not well expressed you already understand the request for help.)
Theorem: Given a manifold $M$ equipped with a metric $g$ and possessing at least one non-trivial isometry $\...
- 772
1
vote
1
answer
206
views
Static Spacetimes
I am reading Wolfgang Rindler's Relativity. At the beginning of the chapter on stationary or static spacetimes he says:
"We now define the stationarity of a lattice by the following light-...
- 455
0
votes
1
answer
231
views
Possible spherically symmetric solutions with a cosmological constant
Why de sitter and Schwarzschild de sitter, and anti de sitter and Scharzschild anti de sitter are the only possible spherically symmetric solutions with a cosmological constant? I have read this fact ...
- 189
4
votes
1
answer
622
views
Proof of Birkhoff's Theorem
I have a question concerning the proof of Birkhoff's theorem in Sean Carrolls book. I am stuck at the part where he shows that there are no cross-terms (in the metric) between $(a,b)$ and $(\theta, \...
- 317
25
votes
1
answer
8k
views
How to prove that a spacetime is maximally symmetric?
In Carroll's book on general relativity ("Spacetime and Geometry"), I found the following remark:
In two dimensions, finding that $R$ is a constant suffices to prove that the space is maximally ...
- 16.4k
4
votes
4
answers
2k
views
Are the principles of space-time homogeneity and Isotropy independent of one another?
Einstein in deriving the Lorentz transformations, used the principles of space-time homogeneity and Isotropy. Does space-time isotropy follow from space-time homogeneity or are they completely ...
- 3,108
2
votes
1
answer
203
views
Symmetries of spacetime and objects over it
I guess according to mathematical didactic, we first think of spacetime as a set and we reason about elements of its topology and then it's furthermore equipped with a metric. Appearently it is this ...
- 8,523