# Tagged Questions

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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### How to measure time in presence of a strong gravitational field? [duplicate]

I need an operative definition of "measuring time in general relativity" that takes in consideration also the presence of strong gravitational fields between me and clock, able to deviate the light ...
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### Do time and spatial derivative under a 3+1 decomposition commute?

After a certain 3+1 decomposition of the space-time, the derivative of time part and spatial part separate. Let's denote them by $d_t$ and $\partial_\mu$. Here the spatial derivative is covariant but ...
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### Worldsheet metric & event horizon

Given a certain metric $g_{\alpha \beta}$ (not necessarily diagonal) in which $g_{\tau \tau}=0$ for a certain function, is there any way of determining if there is a singularity in that point, or if ...
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### Rigorous derivation of general relativity from first principles

What is the minimal set of axioms required to derive the mathematical formulation of General Relativity from first principles? What are these first principles? How does such a derivation go step by ...
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### Variation with respect to the metric and other tensors

When varying an action with respect to tensors and the metric, I'm afraid I get confused as how to one organizes the Lagrangian and then performs the variation. Take for example, the following example ...
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### “Measure of time in general relativity” [duplicate]

Suppose to be in an arbitrary gravitational field and you are moving in it arbitrarily with a clock in your hand. In this general situation I ask: if I read the positions of the hands of the clock, ...
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### Gauss-Weingarten equation

In E Poisson "A relativist tool kit" p.75 it says that the Gauss-Weingarten relation is: $$e^{\alpha}_{a;\beta}e^{\beta}_{b}=\Gamma^{c}_{ab}e^{\alpha}_{c}-\epsilon K_{ab}n^{\alpha}$$ We have the ...
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### Signature of $f: \Lambda^2(\mathbb{R}^4) \times \Lambda^2(\mathbb{R}^4) \to \mathbb{R}$, $f(\omega, \omega') = \omega \wedge \omega'$ [closed]

Define$$f: \Lambda^2(\mathbb{R}^4) \times \Lambda^2(\mathbb{R}^4) \to \Lambda^4(\mathbb{R}^4) \cong \mathbb{R}, \quad f(\omega, \omega') = \omega \wedge \omega'.$$ What is the signature of $f$? ...
I have a (simple) question about the induced metric $h_{ab}$. In Poisson E.A. (a relativist toolkit) it says in p. 62 that the induced metric $$h_{ab}=g_{{\alpha}{\beta}} \frac{\partial x^{\alpha}}{\... 0answers 30 views ### How conclusive is “Gravitational red-shift Gedanken”? The gedanken goes as you take a particle of mass m at a height H. Then let it fall to gain the velocity (approximately)\sqrt{2gH} when it reaches the ground. Convert the particle into a photon ... 1answer 73 views ### How do you actually use the geodesic equation? The geodesic equation used in general relativity is the following:$$ {d^2 x^\mu \over ds^2} =- \Gamma^\mu {}_{\alpha \beta}{d x^\alpha \over ds}{d x^\beta \over ds}. $$It states that the ... 2answers 185 views ### Do gravitational waves have entropy? We know, according the current understanding of black holes and General Relativity, as well as quantum fields in General Relativity, that black holes have an entropy proportional to the area of the ... 1answer 37 views ### Are the quasinormal modes scalar quantities? I am studying the so-called quasinormal modes (QNMs) in the context of the AdS/CFT correspondence and I got stuck. For instance, if I choose a weird patch of coordinates for the, say, AdS5-... 2answers 106 views ### Flat space Solution of Einstein Field Equation Does a trace-free energy-momentum tensor T_{\mu}^{\mu} = 0 ensure that the Einstein's field equations have a flat space solution? 2answers 68 views ### Two Black Holes held stationary by EM forces If two black holes with large enough mass (so that the tidal forces are minimal and the intersection is large) that are held apart by like charges (saddle point stability). Imagine the black holes in ... 1answer 62 views ### Torsion in kerr black holes In General Relativity, we generally assume that the derivative operator is torsion-free, i.e., second covariant derivatives commute on functions. However, in Kerr black holes, spacetime is dragged (... 1answer 37 views ### Do the energies of cosmic rays approach infinite at the event horizon of a black hole? Let's assume an observer orbits close to a black hole, he is not alone, massive cosmic rays, like electrons and protons and other kind of space dust comes from the outer space and may hit him. Since ... 0answers 29 views ### Going to the Einstein frame in f(R) theories First of all thank you for your time! I have a question that I can't solve. In every review that I read, I find that when you want to go to the Einstein frame in a f(R) theory what you have to do ... 0answers 39 views ### Schwarzschild metric, speed of ball as measured by observer who catches the ball, just before ball is caught? [closed] Inspired by this question here. The Schwarzschild metric, describing the exterior gravitational field of a planet of mass M and radius R, is given by$$ds^2 = -(1 - 2M/r)\,dt^2 + (1 - 2M/r)^{-1}\,...
Schwarzschild metric solution presents two singularities. An apparent one at $r=2GM$ and a real one at $r=0$. It is known that everything freezes at the event horizon from an outside observer point of ...