# Questions tagged [general-relativity]

Questions related to the mathematical aspects of Einstein's theory of relativity. For the physics and its interpretations, please ask at the physics.SE. You may also consider the tags (differential-geometry) and (pde).

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### Why do we need to use the chain rule in the transformation of a partial derivative of a vector component from different coordinate systems?

Let us consider the partial derivative of a vector component $A^i$, this is $\partial_jA^i = \frac{\partial A^i}{\partial X^j}$ We also know that we can write the transformed contravariant vector ...
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### Killing vectors in Minkowsky Metric

Firstly, I know this is a physics-related problem, and I have posted here, but the physics forum seems so much more empty then this one, so here it goes: I was in the process to find the Killing ...
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### How to prove that a Riemann Manifold is conformally flat?

In Ray D'Inverno's book - "Einstein's Relativity" he states a theorem that says the following - "Any two-dimensional Riemann manifold is conformally flat". How can I prove this? I ...
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### Riemann curvature tensor identity proof

Let $R_{abcd}$ be the Riemann curvature tensor defined by a torsion free and metric compatible covariant derivative. Ultimately I am trying to prove that $R_{abcd} = - R_{abdc}$ The prove in my ...
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### Can you use black hole theorems to solve navier stokes problem?

To answer whether the navier-stokes equations don't "blow up" for some initial input. It seem like the same type of problem as to whether a particle in GR will hit a singularity. Except in ...
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### Plane-fronted (gravitational) waves

What is the meaning of plane-fronted gravitational waves? and how it can be a generalization of plane waves? I could not imagine the wave with variable wave-vector, and the importance of this ...
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### The metric coefficients in cylindrical coordinates are (a) $(1,1,1)$ (b) $(1,0,1)$ (c) $(1,r,1)$ (d) neither?
In Differential and Riemannian Geometry we study metric cylindrical coordinates $(r, \theta, z).$ I am preparing its Multiple choice questions, Q. The metric coefficients in cylindrical coordinates ...