Questions tagged [general-relativity]
For questions about mathematical problems arising from general relativity, the branch of physics which provides and studies the currently accepted geometric description of gravity.
24 questions from the last 365 days
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What is the difference between the foliation of a manifold and a mere partitioning? [closed]
I'm unable to visualize a partitioning that isn't also a foliation, and I need to so I can understand The Stretched Horizon and Black Hole Complementarity
In particular, I don't understand how curves ...
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Tensor component calculation
First of all, this question may be more suited for the Math stack exchange site. If anyone finds this question irrelevant here, please transfer to the relevant site.
Recall that in terms of Weyl and ...
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Categorical General Relativity
What are some good references for GR from a categorical point of view?
This is essentially just a big-list reference request.
I'm aware that the subject exists and can do some basic sleuthing to find ...
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1
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Non-inertial frames of reference in empty space
Imagine that somebody wants to generalize special relativity to non-inertial frames of reference. For example I am going around a point and the metrics of space is non-Euclidean from my point of view. ...
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Mathematical explanation for connections on gauge bundles in curved spacetime for spinors
I asked this question https://physics.stackexchange.com/questions/820924/is-tetrad-postualte-independent-of-gauge-field
Here is what I know, $g_{\mu \nu} = e^{a}_{\mu} e^{b}_{\nu} \eta_{ab}$ and the ...
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Quasilinear wave equations without (weak) null conditions and conjectures
I have found that most works on quasilinear wave equations require, at least, the (weak) null condition. There are only a few works without this condition, such as "Shock Formation in Small-Data ...
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Possible obstructions to global Wick-rotation in distinguishing spacetimes
Take the time-orientable $3+1$ dimensional spacetime $(M,g)$ that is locally Wick-rotatable at any arbitrary point $p \in M$ to a Riemannian manifold $(N,h)$.
Local Wick-rotatability of $(M,g)$ ...
- 612
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Are causally isomorphic spacetimes Wick-related?
Take the time-orientable spacetimes $(M_1,g_1)$ and $(M_2,g_2)$ that are locally(to be clarified below) Wick-related and both are globally Wick-rotatable(to be clarified below) to the same Riemannian ...
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Does there exist an electromagnetic analogue of Einstein's field equations?
This will look like a physics question but it doesn't have anything to do with reality so its a vague math question if anything.
I recently learned about gravitoelectromagnetism which describes an ...
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Is the topological dimension of spacetime fixed for causally isomorphic spacetimes?
Suppose time-oriented spacetimes $(M_1 , g_1)$ and $(M_2, g_2)$ are not homeomorphic under their manifold topologies $\mathcal{M}_1$ and $\mathcal{M}_2$ respectively.
The Lorentzian metrics $g_1$ and $...
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Lorentzian norm of the covariant derivative of a vector field is zero
Let $Y$ be a vector field on a Riemannian manifold $(M, g)$. If $g(\nabla Y, \nabla Y)=0$, then $Y$ is covariantly constant, i.e. $\nabla Y=0$.
Now, let $V$ be a vector field on a Lorentzian manifold $...
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Order isomorphism + manifold homeomorphism => path topology homeomorphism?
Suppose time-oriented spacetimes $(M_1 , g_1)$ and $(M_2, g_2)$ are homeomorphic under their manifold topologies $\mathcal{M}_1$ and $\mathcal{M}_2$ respectively.
Let's call this map $\phi: (M_1, \...
- 612
3
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Topology and local isometry, spinning cosmic string
Suppose one is given the spacetime $(M,g)$ where $M$ is a fixed differentiable manifold and $g$ is a Lorentzian metric whose local expression is:
$$g= -(dt + a \, d \phi)^2 + d\rho^2 + \kappa^2 \rho^2 ...
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What is the "intrinsic reason" for the failure of Schwarzschild coordinates in general relativity?
It is well known that the Schwarzschild metric fails at r = 2M (in units where c = G = 1) and this is the result of choosing "bad" coordinates. I find this surprising because the coordinates ...
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Definitions of weak solutions for quasilinear wave equations
I am learning the shock problem for the balance system (perhaps not conserved, see, e.g., "Ingo Muller, Tommaso Ruggeri. Rational Extended Thermodynamics") and just have a question on the ...
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On sub-maximally symmetric Riemannian spaces
Is there a 4-dimensional Riemannian manifold with 8-dimensional isometry group?
Context: Guido Fubini (Annali di Mat., ser. 3, 8 (1903) 54) shows that the dimension $n$ of the isometry group of a $d$-...
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Prove the orthogonality of vector spherical harmonics
We define
$S_a^{lm} = \Big( - \frac{1}{\sin \theta} Y^{lm}_{,\varphi}, \sin \theta\ Y^{lm}_{,\theta} \Big)$
$Y_a^{lm} = \Big( Y^{lm}_{,\theta}, Y^{lm}_{,\varphi} \Big)$
to be the axial vector ...
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Handling degenerate planes in pseudo-Riemannian geometry: impact on sectional curvature and comparison theorems
I've been studying Riemannian and pseudo-Riemannian manifolds and came across an intriguing point regarding the definition of sectional curvature in both geometries.
In pseudo-Riemannian geometry, for ...
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On the linearized evolution equations in general relativity
The following puzzles me already for quite some time: In mathematical relativity, especially in the discussion of the Cauchy problem, one usually works in the so-called ADM-Formalism, in which one ...
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What is the Lebesgue covering dimension of this topological space?
Take the 4 dimensional time-oriented spacetime $(M,g)$ such that it's not strongly causal.
Take the induced topology defined by the Lorentzian metric called Alexandrov topology.
This topology matches ...
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2
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Is the Gödel universe Wick rotatable?
Take Wick rotatability being as the way defined in the following article by Helleland and Hervik:
Christer Helleland, Sigbjørn Hervik, Wick rotations and real GIT, Journal of Geometry and Physics 123 ...
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How causal is a strongly causal purely electric spacetime?
Take a generic Lorentzian spacetime $(M, g)$ where $M$ is a time-oriented 4d manifold and $g$ is the Lorentzian metric that is strongly causal and purely electric.
According to this answer:
Is every ...
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Is a Wick rotatable spacetime necessarily strongly causal?
There are a few viable ways to formulate Wick rotatability that preserve distinct features.
One is mentioned in the post:
Obtain Lorentzian manifolds from Riemannian ones by Wick rotation
There's also ...
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Is every strongly causal spacetime purely electric?
Take a time 4-dimensional orinted Lorentzian manifold $(M,g)$.
A spacetime is called Strongly Causal at point $p$ if and only if for every neighbourhood $U$ of the point $p$ there exists a ...
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