All Questions
93
questions
4
votes
3
answers
408
views
Confusion over what constitutes a uniform gravitational field in relativity
Suppose we have some observer moving upwards with a constant proper acceleration, by the equivalence principle this is the same as the observer remaining stationary in a gravitational field, like ...
- 312
3
votes
2
answers
106
views
References on Newton-Cartan Gravity
I'm interested in learning a bit about Newton-Cartan gravity, and I would like some references on the topic. I am already familiar with differential geometry and general relativity, so those could be ...
2
votes
0
answers
69
views
Compute the difference between the Christoffel symbols compatible with two different metric tensors
Imagine I have two metric tensors $g_{\alpha\beta}$ and $\hat{g}_{\alpha\beta}$ on the same manifold M and two metric-compatible, torsion free Christoffel symbols $\Gamma^{\mu}_{\alpha\beta}$
$$\Gamma^...
- 4,827
2
votes
0
answers
135
views
Einstein's gravity Lagrangian invariance under the change of differential structure
I came across an article claiming the appearance of singularities in the energy-momentum tensor $T_{\mu \nu}$ as a result of changing the differential structure:
I wonder what symmetry or current (in ...
- 1,268
3
votes
0
answers
92
views
Can a CTC contaning spacetime be purely electric?
Take a time-oriented Lorentzian manifold $(M, g)$ where $M$ is a topological 4-manifold and $g$ a Lorenzian metric.
Assume such a spacetime contains a CTC.
Since the manifold is time-oriented, one can ...
- 1,268
0
votes
1
answer
112
views
Sean Carroll, can I skip to chapter 8 after chapter 4? [closed]
For anyone who has studied the book 'An Introduction to General Relativity Spacetime and Geometry' by Sean Carroll, can I study chapters 1 to 4 (which do differential geometry & field equations it ...
- 35
1
vote
1
answer
177
views
Dust solutions in general relativity
What is the precise definition of a dust solution in general relativity?
If the Einstein tensor of a metric has only the first diagonal term non-zero, it that sufficient for that solution to be called ...
- 97
1
vote
0
answers
161
views
Why does general relativity assume that the torsion is equal to zero?
I do not understand why the torsion is set equal to zero in the general theory of relativity. The geodesics would be the same. Is there even a way to test it?
Pg 250 from the 2017 edition of MTW says
...
- 391
5
votes
2
answers
312
views
The limit of GR with infinite speed of light $c$
Just answer what you can. I don't mean the zero curvature flat space time version. I know that the Einstein Field equations use $c$ as a constant, but what would the universe be like if gravity was ...
- 83
5
votes
1
answer
345
views
Allowed Topologies for General Relativity
Studying the ADM formulation of General Relativity the ADM splitting comes out from the assumption that the spacetime is globally hyperbolic.
From that assumption thanks to Geroch's theorem, it is ...
- 1,611
2
votes
0
answers
76
views
Newton-Cartan from GR
How does EFE reduce to Newton-Cartan Field Equation $R_{tt}=4\pi G \rho$ in Newtonian Limit? I understand its direct derivation from geodesics in weak field, what I am curious about is how EFE reduces ...
- 1,161
3
votes
2
answers
468
views
Reformulate Einstein equations to make them linear
Is it possible to reformulate the Einstein equation in terms of a new variable, say $k_{\mu\nu}$ in terms of the metric $g_{\mu\nu}$, in order to make the Einstein equations linear in $k_{\mu\nu}$?
- 758
1
vote
1
answer
188
views
Null surfaces in Lorentzian manifold
Null Hypersurface of Lorentzian Manifold: A hypersurface that admits a null-like normal vector field($N^a$) to it. i.e. $g_{ab}N^a N^b=0$ (metric signature$(-1,1,1,1,...)$)
In Minkowski spacetime the ...
- 27
2
votes
0
answers
181
views
Variation of gravity in tetrad (vierbein) formalism using xAct or other computer algebra for wolfram language
I recently did some calculations in teleparallel gravity, where the fundamental variables are tetrad and flat spin connection. The Lagrangian density of teleparallel gravity is given by
\begin{...
- 21
1
vote
0
answers
62
views
Wald: 2-dim Covariant Derivative for Null Hypersurfaces
On pp. 221-222, Wald introduces the 2-dim "hatted" manifold of null geodesics. He moves from 9.2.30 to 9.2.31 and he is allowed to do so because the tensors have the special properties that ...
- 61