All Questions
93
questions
4
votes
2
answers
8k
views
Maximally symmetric spaces
In GR, what is the most precise definition of a maximally symmetric spacetime?
Also, we study about the temporal boundary of dS space, and a spatial boundary of AdS space, but aren't these spaces ...
- 1,182
1
vote
1
answer
69
views
Properties of space-time intervals derived by symmetry principles
In many books about special relativity I found the following arguments:
1) because the transformations between two inertial reference frames $K$ and $K'$ are linear and because if $\Delta s^2 = 0 $ ...
- 433
1
vote
1
answer
553
views
5
votes
1
answer
158
views
Assuming a fixed total mass, will the spacetime geometry outside a spherical mass distribution depend on the shape (of the distribution)?
Consider two independent spheres of equal masses but of different radius and in different spacetimes. The first sphere is less dense than the second one, i.e., it has a larger radius. For example, if ...
- 51
5
votes
1
answer
203
views
Reconstructing Minkowski spacetime from its Killing-algebra
Assume the following situation is given:
We know that there is a 4 dimensional pseudo-Riemannian manifold $(M,g)$ (for now, of unknown signature) and there are 10 Killing vector fields, indexed as $...
- 11.3k
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
6
votes
1
answer
145
views
Will an eventual discreteness of spacetime have consequences in the light of Noether's theorem?
No doubt Noether's theorem holds for the symmetry of translations in space and time. But what if we zoom in on very small lengths and times, and spacetime maybe becomes discrete? Will this have ...
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
1
vote
1
answer
159
views
Why doesn't the universe look symmetrical?
If the universe was a dot lets say a point, and that dot expanded equally from all sides, then shouldn't the universe look more symmetric, maybe indentical, from that dot all around?
9
votes
2
answers
2k
views
Killing tensor in the Kerr metric
It was famously shown by Carter that the Kerr metric possesses a 4th non-obvious constant of the motion, derived from the separability of the Hamiltonian. This constant is related to a Killing tensor.
...
- 1,751
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
1
vote
0
answers
91
views
BMS supertranslations and integral identity in arXiv:1603.07706
Looking at the paper 1603.07706 we see that infinitesimal BMS supertranslations are generated by:
$$
\xi = f\partial_u - \frac{1}{r}\left(D^zf\partial_z + D^\bar{z}f\partial_\bar{z}\right) + \frac{1}{...
- 570
2
votes
1
answer
538
views
Deriving the Minkowski Metric from homogeneity of space-time and the isotropy of space
In this wikipedia page, it says that one can derive the spacetime interval between 2 arbitrary events from the second postulate of special relativity, together with the homogeneity of spacetime and ...
- 504
4
votes
1
answer
622
views
Proof of Birkhoff's Theorem
I have a question concerning the proof of Birkhoff's theorem in Sean Carrolls book. I am stuck at the part where he shows that there are no cross-terms (in the metric) between $(a,b)$ and $(\theta, \...
- 317
0
votes
2
answers
873
views
How to find the isometry group of space-time?
I am given the next pseudometric:
$$
ds^2=dt^2-\frac{r^2+a^2 \cos^2 \theta}{r^2+a^2}dr^2-(r^2+a^2)\sin^2 \theta d\phi^2-(r^2+a^2\cos^2 \theta)d\theta^2.
$$
How to find the isometry group for such ...
