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 ...
2
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1answer
71 views

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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1answer
113 views

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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0answers
46 views

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 ...
3
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0answers
50 views

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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1answer
52 views

A Calculation in Padmanabhan's Book

I have seen this in Padmanabhan's book. How can I verify this: $$d\Sigma_{mn}=\frac{1}{2!}\epsilon_{mnab}\frac{\partial(x^a,x^b)}{\partial(\theta,\varphi)}d\theta d\varphi=\epsilon_{mn\theta\varphi}r^...
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20 views

What are Pre-requisites for General Relativity [duplicate]

I have a background in Electrical engineering. However, I have a passion for physics and want to do my Masters in Physics. I was hoping to do some sort of self - study in topics that I have not ...
4
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1answer
83 views

Killing tensor in Minkowski space

I'm trying to solve the Killing tensor equation $\nabla_{(a}K_{bc)} = 0$ in Minkowski space. I'd like to generalise the method we use to find Killing tensors in Minkowski space. We can take $\...
3
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2answers
116 views

Is a spacetime of constant positive curvature just a 4-hypersphere?

In discussions of basic cosmological models, I don't see "spacetime of constant positive curvature" described more simply as a "4-hypersphere". What am I missing?
4
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2answers
99 views

If maximum speed limit $c$ is made infinite, will general theory of relativity become equivalent to Newton's gravitational theory?

We know that special relativity tends to become equivalent to classical theory of relativity as the speed limit of nature becomes infinite. If this happens, clock will tick at the same rate ...
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2answers
68 views

Is frame drag the magnetic part of gravity? [closed]

Like moving charged mass creates an magnetic field, does moving mass also creates a magnetic field associated with moving (accelerated) mass? And if so, why does the mass have to accelerate, while in ...
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1answer
66 views

Gravitational waves (linearized gravity) [closed]

Even in the Schwarzschild metric we can write $g_{uv}=\eta_{uv}+h_{uv}$ where $h_{uv}$ is very small. So after some coordinate transformation (using gauge freedom) we can simplify the Einstein ...
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0answers
36 views

What expression of Ricci tensor should we choose in order to obatin a correct field equations?

I have doubt regarding the choice of the Ricci tensor $R_{ij}$. I have seen many books and papers use the expression $R_{ij}=\Gamma^i_{jp,i}-\Gamma^i_{ji,p}+\Gamma^i_{in}\Gamma^n_{jp}-\Gamma^i_{pn}\...
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1answer
86 views

Wave operator applied to electromagnetic field tensor

I'm trying to understand an argument in "An introduction to general relativity" by Hughston and Todd (p37). Let $F_{ab}$ be the electromagnetic field tensor, I'm trying to show: $$\Box F_{ab} = -4 \...
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1answer
46 views

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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0answers
36 views

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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1answer
35 views

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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0answers
89 views

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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0answers
34 views

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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1answer
72 views

“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, ...
0
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0answers
52 views

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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0answers
36 views

Nature of the singularity in the Taub-NUT metric

Consider the Taub-NUT metric $$ds^2=-V(dt+2N(1-\cos\theta)d\phi)^2+\frac{1}{V}(dr^2)+(r^2+N^2)(d\theta^2+\sin^2\theta{}d\phi^2),$$ where $$V=\frac{(r-r_+)(r-r_-)}{(r^2+N^2)} \qquad r_{\pm}=M\pm \...
2
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2answers
105 views

What is the singularity of an actual collapsing black hole?

In most general relativity texts, the singularity is treated as a point removed from the manifold, to avoid having to deal with the infinite curvature of the Ricci scalar. But in the case of a more ...
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3answers
96 views

Covariant Derivative of Kronecker Delta

I am reading Carroll's book on GR right now, and I ran into a little trouble in his chapter 3 on curvature. He is establishing the properties of the covariant derivative, and claims that the fact that ...
2
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1answer
49 views

Charge without charge and non-traversable wormholes

My question concerns the theory proposed in this classic paper by Misner and Wheeler. In the paper, the authors propose the idea of "charge without charge"--namely, that positive and negative ...
2
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1answer
94 views

How much Gravity is required to stop time?

Clocks free of gravitational influence run faster than those experiencing gravity. Is it possible for gravitational influence to bring time to a stop? Additionally can acceleration affect clocks in ...
0
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1answer
47 views

EFE and Local Minkowski

Suppose we view the Einstein Field Equations (EFE) in the context of a boundary value problem with a given stress-energy tensor and boundary conditions. The problem is solved by finding a pseudo-...
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1answer
77 views

Global Hyperbolicity in spacetime Manifold [closed]

If space time is timelike or null geodesically incomplete but cannot be embedded in a larger spacetime then we say that it has singularity. What does incompleteness means here?
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1answer
35 views

Conserved quantity in a spacetime with Killing vector

I am trying to prove that that the expression $Q=-\frac{1}{\kappa}\int_{S_\infty} \nabla^i \xi^k \mathrm{d}\sigma_{ik}$ is a conserved quantity for a spacetime with Killing vector $\xi^i$ where $S_\...
5
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1answer
73 views

Coupling a spinor field to a preexisting scalar field?

So I'm not a physicist, but I'm thinking about a mathematical problem where I think physical insight might be useful. We're working on a Riemannian manifold $(M,g)$ (positive definite metric) with a ...
2
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2answers
85 views

What is the difference between time and space in general relativity?

I know that similar questions have been asked before, I will try to be specific. In special relativity time is the coordinate with minus sign in metric tensor. In general relativity the components of ...
0
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1answer
39 views

Energy required to accelerate from different reference frames

So I've recently been studying relativity a lot trying to understand it and I feel like I grasp most things conceptually but I have one issue I've been trying to understand for the last couple days ...
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2answers
156 views

Can the question of a gravitationally accelerated charge radiation be tested experimentally?

I know that the question of radiation from a gravitationally accelerated charge has been discussed extensively at Does a charged particle accelerating in a gravitational field radiate?. Yet the ...
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0answers
30 views

Are general coordinate transformations and diffeomorphisms the same? [duplicate]

Infinitesimal diffeomorphisms $x{}^\mu \rightarrow x{}^\mu + \xi{}^\mu$ (with $\xi{}^\mu \ll 1$) change geometric objects by means of the Lie derivative, that is, $X \rightarrow X + \mathcal{L}_\xi \, ...
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0answers
30 views

Coordinate time difference between emiting and detecting a photon in bent spacetime

Consider an arbitrary non-trivial metric $g_{ij}$ - like the Schwarzschild metric. Now, consider two observers $A$ and $B$, staying at fixed radii $R_A$ and $R_B$, respectively, with $R_A > R_B$. ...
6
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2answers
106 views

Will accelerated observer see radiation from the charge that is at rest in observers's frame?

So I had a huge debate about this with my friends. Imagine that you are in a non-inertial frame of reference. For simplicity, assume that frame is accelerated along x-axis. You have held a charge in ...
6
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1answer
85 views

Conformal Gravity

Lubos, in his comment to a question, says that (http://physics.stackexchange.com/q/61281) First of all, one can't gauge a symmetry without modifying (enriching) the field contents. Gauging a ...
3
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0answers
96 views

Scalar Curvature of a Conformally Flat Metric

Suppose that you have a metric $g_{\mu\nu}=\phi^2\eta_{\mu\nu}$ for some function $\phi$. There is a standard formula for what the scalar curvature $R$ looks like in terms of $\phi$, which is given by ...
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31 views

Linearized Einstein equation on a general background metric

All of my texts only give the Linearized Einstein equation on the Minkowski background so I thought I'd try and figure it out by hand today. Using the standard perturbation $h_{\mu\nu}$ and denoting ...
10
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2answers
917 views

Orbits around the Photon sphere of a black hole (Schwarzschild coordinates)

This is a follow-up question to the answer given at What is the exact gravitational force between two masses including relativistic effects?. Unfortunately the author hasn't been online for a few ...
0
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0answers
36 views

How is gravitational time dilation different from time dilation due to differences in speed? [duplicate]

This is what I understand from what I've been reading online: In the derivation for the gravitational time dilation equation, $$t = t_0\sqrt{1-\frac{2GM}{rc^2}}$$ we use the special relativity ...
2
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1answer
74 views

Are the Schwarzschild metric and the Geodesic Equation relevant in the context of the Earth? [closed]

The geodesic equation used in general relativity is the following: $$ {\mathrm d^2 x^\mu \over \mathrm ds^2} =- \Gamma^\mu {}_{\alpha \beta}{\mathrm d x^\alpha \over\mathrm ds}{\mathrm d x^\beta \...
5
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1answer
70 views

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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0answers
36 views

Induced metric is a scalar for transformation from $x\to x'$? (Poisson E.A p.62)

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}}{\...
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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 ...
3
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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 ...
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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 ...
2
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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-...
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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?
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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 ...