# 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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### Gravitational wave energy fluxes and bracket averaging notation

Typically the rate of energy loss due to gravitational waves is given in the form (e.g. MTW or Eq 33 of these notes), $$\dot{E} = - \frac{1}{5} \langle \dddot{I}_{jk} \dddot{I}_{jk} \rangle$$ where ...
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### General Relativity - Confusion between choosing basis (orthonormal & coordinate) and coordinate transformations

I am reading the book 'Gravity' by Hartle and presently I am at the section discussing orthonormal and coordinate bases. I am confused about a few points I had read previously and can't exactly ...
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### Confused about the gauge transformation of the amplitude tensor for gravitational waves

Far away from the field sources, where the energy-momentum tensor $$T_{mn}=0 \tag{m,n=0,1,2,3}$$ The linearized EFE becomes $$\Box \bar h_{mn}=0 \tag{1}$$ where $\bar h_{mn}$ is the trace-reverse ...
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### Graviton propagator, and Gauss-Bonnet gravity

Let's say we consider Einstein's Lagrangian from GR. In linearized gravity, we would expand the Ricci scalar to quadratic order in the perturbation parameter to find the propagator. My question is as ...
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### Doubt regarding cross sections of a Killing horizon

I was reading RĆ”cz and Wald's paper 'Extensions of spacetimes with Killing horizons' and they are frequently referring to a cross section of a Killing horizon (a three surface where the norm of the ...
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### Conformal compactification of spacetimes

Iām looking answers and/or references concerning the following questions about conformal compactification. Given a $d$-dimensional spacetime $(M,g)$ (or simply just for $d=4$): Does the conformal ...
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### When is it possible to diagonalize a metric tensor with a coordinate transformation?

The question is a mathematical one, but I believe more likely to find here interested people, as it is relevant for GR. The problem arose for Kerr space-time and Boyer-Lindquist coordinates, where the ...
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### Harmonic Oscillator and Shifts in Derivative Operators

What symmetries/symmetry breaking arises from shifts in the derivative operators? To explain what I mean let's study an example. The classical one particle one dimensional harmonic oscillator has the ...
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### Do white holes encode the future evaporation of the black hole?

In General Relativity, white holes arise when one formulates Maximal extensions (the process by which coordinate singularities are mapped to new non-degenerate coordinates) to a geometric solution (...
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### Elevator moving near the speed of light

Imagine that you are in an elevator that is moving downward at a constant speed that is near the speed of light (let's say close to the surface of the earth: toy problem, needless to say). Now say ...
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### Constraint equation for Einstein-Hilbert action in Light-cone gauge

In Light cone coordinate system $(+,-,i)$, where $i=1,2$, the light cone coordinates are defined as $x^{\pm}=\frac{x^0 \pm x^3}{\sqrt{2}}$, if we consider the $+$ coordinate to be our "timelike" ...