All Questions
50
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
1
vote
0
answers
57
views
What are Supertranslations and Superrotations in General relativity, and how does it inform us about a detector at null infinity?
How did I get here?
While drafting my question, I found this very similar question on our site.
Three days ago, I happened upon the concept of supertranslations and superrotations in General ...
- 246
0
votes
0
answers
63
views
Stationary, static and strictly stationary/static?
Consider spacetimes which are asymptotically flat at null infinity.
How to explicitly show that there exists a hyper-surface orthogonal killing vector field $k^{a}$ that is time-like everywhere in ...
- 21
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
3
votes
2
answers
163
views
Static spacetime and metric invariance
I'm studying General Relativity using Ray D'Inverno's book "Introducing Einstein's relativity". I don't understand what the author writes in paragraph 14.3 ("Static solutions") ...
- 65
2
votes
1
answer
143
views
Question on Tolman-Oppenheimer-Volkoff (TOV) equation for time-dependent spacetimes [closed]
Is there a way to conceive a TOV equation, and therefore the stability analysis for a metric like:
$$ ds^2 = -dt^2 + a^2(t,r)\big(dr^2 + r^2d\Omega ^2\big)~?\tag{1}$$
- 3,085
1
vote
1
answer
167
views
What does it mean that the metric is static?
I'm reading the paper Regular phantom black holes where in page 2 (left column) the authors write that "the metric is static where $A(\rho)>0$".
Does anyone know what they mean with the ...
- 2,478
2
votes
2
answers
175
views
Do the Klein bottle and torus topologies break the Lorentz invariance?
According to this preprint, it seems that there are topologies (like the Klein bottle and the torus) that break some symmetries (like the Lorentz and translation invariances).
Is this right? Can they ...
- 2,462
0
votes
0
answers
44
views
Effects of anisotropy and non-homogeneity in the universe's symmetries...?
I was reading Philip W Anderson's essay "More is Different" (https://www.tkm.kit.edu/downloads/TKM1_2011_more_is_different_PWA.pdf) and at some point he links the isotropy and homogeneity of ...
- 2,462
0
votes
0
answers
62
views
Spacetimes where symmetries vary from place to place?
Are there spacetimes or metrics where symmetries (like Poincaré, Lorentz, diffeomorphism, translational... invariances) are only local and the symmetries of one local neighbourhood are not, a priori, ...
- 2,462
3
votes
2
answers
158
views
Are there non-smooth metrics for spacetime?
I found this statement in a discussion about the application of local Lorentz symmetry in spacetime metrics:
Lorentz invariance holds locally in GR, but you're right that it no longer applies ...
- 2,462
0
votes
0
answers
87
views
Spacetimes, metrics and symmetries in the theory of relativity?
I was discussing this paper with a couple of physicists colleagues of mine (https://arxiv.org/abs/2011.12970)
In the paper, the authors describe "spacetimes without symmetries". When I ...
- 2,462
3
votes
1
answer
212
views
Is spacetime flat inside a rotating hollow sphere in general relativity?
Newton himself proved the Shell theorem, stating that inside a hollow sphere there is no gravitational force on a point mass. This theorem relies on the fact that Newtonian gravity falls off like $1/r^...
- 9,910
1
vote
1
answer
136
views
Is the non-simply connected version of AdS space a maximally symmetric spacetime?
A common construction of anti-de Sitter space is the following:
Start with the flat five-dimensional manifold with metric $ds_5^2 = -du^2 - dv^2 + dx^2 + dy^2 + dz^2$.
Consider the hyperboloid ...
- 48.4k