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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2answers
54 views

Locally remove a gravitational field

Let $K$ be an inertial frame of reference on $\mathbb{R}^3$ and $g=g(t,x)$ a nonuniform and nonstatic gravitational field. How I can choose a system of reference $\bar K$ such that mechanical effects ...
1
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1answer
51 views

How to calculate the free energy in curved space?

To study the Hagedorn temperature of string near a black hole, we need to calculate the free energy in curved space. This is can be done calculating a torus path integral, but I want to know if an ...
0
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1answer
54 views

Qualitative picture or reference for a Lemaître's Cold Big Bang theory

Warning: please, consider this question to be motivated by historical curiosity or as an exercise in model-building. I believe this cannot be considered non-mainstream physics as it was very much ...
1
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1answer
69 views

Uncommon tensor notation $\partial_{(\mu}\xi_{\nu)}$

I came across this expression for the change in a metric under an infinitesimal gauge transformation $\epsilon\xi^\mu$. $$h_{\mu\nu}' = h_{\mu\nu}+2\epsilon\partial_{(\mu}\xi_{\nu)}$$ What does the $...
53
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8answers
12k views

If the speed of light is constant, why can't it escape a black hole?

When speed is the path traveled in a given time and the path is constant, as it is for $c$, why can't light escape a black hole? It may take a long time to happen but shouldn't there be some light ...
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2answers
107 views

How does gravity truly work in the bend of spacetime?

If gravity is caused from the bend in space time from a large mass, why do all objects fall towards earths center and not strait down to below earth? Sorry i am not an expert in any fields just trying ...
2
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1answer
52 views

GR Verification for a Charged Black Hole

For a charged ($Q$) rotating ($L$) mass ($M$), the Kerr-Newman equations give the angular deflection of light. Has there been observational verification (I would prefer to use only the angular ...
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1answer
62 views

Covariant derivative [closed]

Hi, Could you explain to me why the subtraction of vector at some point and parallel transported vector is covariant derivative vector. How is it possible
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1answer
44 views

Does the FRW metric imply spacetime scales?

The FRW metric can be written in conformal co-ordinates to give: $$ds^2=a^2(\eta)(-d\eta^2+d\mathbf{\Sigma^2}),$$ where $\eta$ is the conformal time and $\mathbf{\Sigma}$ ranges over 3-dimensional ...
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1answer
44 views

Symmetry group of FLRW metric

$$ g = dt^2 - a^2(t) (dx^2+dy^2+dz^2) = dt^2-a^2(t)(dr^2+r^2d\Omega^2)$$ So this is my metric. What is the symmetry group of it? I think that my Killing vectors are 3 translation vectors: $$K_i = \...
2
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1answer
81 views

What is the latest science on closed timelike curves? [closed]

In Scientific American (Sept 2014), Lee Billings writes: Lloyd, though, readily admits the speculative nature of CTCs. “I have no idea which model is really right. Probably both of them are wrong,”...
1
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1answer
49 views

Inverse metric in Newtonian limit of GR

I am reading Carroll's book. So looking at the Newtonian limit we write $g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}$ where $h_{\mu\nu}$ is some small perturbation. He says that because $g^{\mu\nu}g_{\nu\...
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2answers
51 views

Friedmann equations with $w <-1$

Let's consider a flat universe with an FRW metric with scale factor $a(t)$, with some matter content. The continuity equation $\nabla_\mu T^{\mu\nu}=0$ combined with assumptions of isotropy and ...
1
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0answers
22 views

Extrinsic curvature for cylinder [migrated]

Suppose we have the following metric describing a cylinder: $$ds^2=ud\rho^2+\rho^2d\phi^2$$ where $u$ is a function of $\rho$. We know the definition of the extrinsic curvature that is, $$K_{ij}=-\...
1
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1answer
94 views

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
votes
1answer
70 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 ...
1
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1answer
106 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 ...
0
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0answers
45 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
49 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
51 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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0answers
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
votes
1answer
81 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
votes
2answers
115 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
97 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
65 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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votes
1answer
60 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}\...
0
votes
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 \...
0
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1answer
45 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 ...
0
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0answers
35 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 ...
0
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1answer
34 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 ...
1
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0answers
75 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? What are good references that detail ...
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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 ...
1
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1answer
68 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
50 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 ...
0
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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 \...
0
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0answers
39 views

Does the rate of observable change within space-time change as time passes?

Mass seems to be one thing the effects the "relativeness of time". Assuming the big bang, if the universe had mass in one central location and the mass is moving away from a singular point it would ...
2
votes
2answers
102 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 ...
1
vote
3answers
91 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 ...
-1
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0answers
21 views

Global Hyperbolicity IN SpaceTime

why space time which admits a Cauchy surface is called globally hyperbolic. I didn't actually understand what does globally hyperbolic physically means.
2
votes
1answer
47 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
votes
1answer
92 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
votes
1answer
46 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-...
-1
votes
1answer
58 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?
1
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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
votes
1answer
71 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
83 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 ...
8
votes
2answers
149 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 ...
0
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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 \, ...