# 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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### What is the additional gravitational term from general relativity given by?

Carroll gives the potential energy in general relativity by $$V(r)=\frac{1}{2}\epsilon-\epsilon\frac{G\,M}{r}+\frac{L^{2}}{2r^{2}}-\frac{G M L^{2}}{r^{3}}$$ My first question is does $V(r)$ have ...
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### Problem 1 Chapter 11 Wald

I'm currently trying to solve problem 1, Chapter 11 of Wald, General Relativity. The request is to derive from the condition $$\tilde\nabla_a \tilde\nabla_b \Omega=0\text{ at }\mathscr I^+,$$ where ...
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### Does space itself fall into a black hole? [duplicate]

Long time ago I heard someone say that it is space itself that falls into a black hole. Yesterday I saw a little animation that suggested the same (although I´m not sure, because the person who put ...
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### What is the connection between the coordinate transformation properties and graphical representation of covariant and contravariant components?

So right now I am studying General Relativity (in particular tensor analysis), and I have a question regarding covariant and contravariant components of a vector. I was taught how to transform ...
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### Centrifugal force in the two body problem?

In the two body problem, the Effective radial potential energy in general relativity is given by $$V(r)=-\frac{G M m}{r}+\frac{L^{2}}{2\mu r^{2}}-\frac{G(M+m)L^{2}}{c^{2}\mu r^{3}}$$ where the ...
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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 $f$? ...
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### 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 ...
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### 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-...
Does a trace-free energy-momentum tensor $T_{\mu}^{\mu} = 0$ ensure that the Einstein's field equations have a flat space solution?