# Questions tagged [general-relativity]

A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

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### Pertubation of Riemann tensor in a general curved space-time

It is a direct and simple question. I am fully developing the perturbation of Einstein Field Equations, and I need to calculate the perturbation of the Riemann tensor. However the background metric is ...
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### What's the relevance of geometric rigidity/flexibility to physics?

I'm currently working on a mathematics research problem in differential geometry that deals with the rigidity of closed manifolds described by non-trivial induced metrics. I'm curious what the ...
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### Numerical Solution for Geodesic Equations in Schwarzschild Spacetime [closed]

I am trying to numerically solve the geodesic equations in Schwarzchild spacetime with a python program. As I couldn't do it on my own, I tried to get help from Chat-gpt but even he failed too. This ...
1 vote
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### Transformation of ADM parameters under diffeomorphisms

I am trying to prove the invariance of the ADM formalism under (infinitesimal) diffeomorphisms. I have checked Wald and other textbooks on the subject but have been unable to find expressions for how ...
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### General Relativity an inevitable consequence of the constancy of light-speed and the equivalence principle: Is this really true?

Quite a long time ago, longer than I'd like to admit, I had heard what is said in the title -- that General relativity is the inevitable result of the constancy of the speed of light and the ...
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### Index position when varying an action with respect to the metric

I'm confused about where we should put tensor indices when we vary an action wrt the metric. For example, if I have in the Lagrangian a term such as $$A_{\mu\nu}B^{\mu\nu},$$ do I necessarily have ...
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### Confusion on the definition of the Christoffel symbols

A common way to introduce the Christoffel symbols is by defining them as determining how the basis vectors change when you translate along your coordinates: \frac{\partial\hat{e}_{(\gamma)}}{\...