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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Wave equation on Schwarzschild background

I am trying to follow the solution of the wave equation for a scalar field on Schwarzschild background from http://batteringram.org/science/gr/scalar_wave.pdf. I have a problem on page 2 where they ...
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202 views

Is there any evidence against the Cosmological Principle?

I have been slowly getting more into math, but haven't gone into differential geometry or anything like that yet, so this question might be basic. Trying to get a deeper understanding of the ...
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89 views

Could electromagnetic charge curve something like spacetime in analogy with general relativity? [duplicate]

Newtonian gravity and electrostatics have the same form; this analogy is extended when we look at full dynamic electromagnetism, and correspondingly "gravitomagnetism". We are quite capable of ...
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Can anyone explain me how time can bend according to Einstein in simple way? [duplicate]

I am just 16 and curious to learn about Theory of Relativity. Can any one explain it simple enough for me to understand? I read that it is bending of time-space or space-time that causes gravity. How ...
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86 views

Path of light as it travels between two black holes

What would happen to light passing through a narrow space between the event horizons of two equal-mass black holes? Would it deviate or follow a straight path?
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66 views

Stress-energy tensor on spacetime satisfying Klein-Gordon equation

Consider the stress-energy-momentum tensor $$T_{\alpha \beta}=(\nabla_\alpha \phi )\nabla_\beta \phi -\frac{1}{2}g_{\alpha \beta}((\nabla^\nu \phi ) \nabla_{\nu} \phi +m^2 \phi^2$$ where the ...
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50 views

Are there any $f(R, T)$ models of gravity?

For the past few months I have been studying $f(R)$ models of gravity. Recently I came cross $f(R, T)$ modified models of gravity. For the past few days I have tried to work out the difference between ...
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77 views

Do metric theories with torsion contradict solar system observations?

Obviously, the answer to this question can be "maybe, if you make the torsion tensor small enough", but my question is, given some "typical" size to the torsion tensor, do the spin-orbit couplings ...
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132 views

Closed timelike curves in the spin-2 gravity formalism

Let's say we take some topologically trivial CTC spacetime, like the Gödel metric: $$ds^2 = -dt^2 - 2e^{\sqrt{2}\Omega y} dt dx - \frac{1}{2}e^{\sqrt{2}\Omega y} dx^2 + dy^2 + dz^2$$ And then I ...
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Question on time dilation [duplicate]

When i studied physics we had this example where someone climbes into a rocked flyes into space comes back the time that passes for him one year time on earth 86 years. I think most know what thinking ...
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82 views

Symmetry of extrinsic curvature tensor

I am trying to solve following problem: In a spacetime of signature (+, −, −, −), let $$ u^au_a = 1, \quad A_{ab} = \nabla_cu_dh^c_{\; a}h^d_{\; b}, \quad h_{ab} = g_{ab} - u_au_b $$ Show that ...
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68 views

Raychauduri equation for Milne universe

I am trying to solve this kind of problem: Consider the Milne model, i.e., the empty $ \kappa = −1 $ Friedmann model. Verify by a direct calculation that the expansion $ \Theta $ of the unit ...
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48 views

Is the Cauchy Horizon of Anti deSitter spacetime stable?

The Cosmic Censorship Conjecture are two mathematical conjectures about the structure of spacetime. In particular the so called Strong Cosmic Conjecture asserts heuristically that generically, ...
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111 views

Does all of spacetime exist?

In Brian Greene’s 2004 book, The Fabric of the Cosmos, he quotes Einstein on the meaning of time, …the distinction between past, present and future is only an illusion, however persistent. ...
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60 views

Gauge freedom in tetrad

I asked the question in the MathOverflow, but didn't get any response. I thought maybe better luck here. I'm reading the following paper about Petrov type D space times called "Type D vacuum ...
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82 views

Can tachyons escape the gravitational pull of a black hole?

Anything that crosses the event horizon of a black hole cannot escape the pull since it has crossed the Schwarzschild radius and thus, the escape velocity is greater than the speed of light, and since ...
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68 views

General relativity and quantum fields evolution in curved space [closed]

There are many cases when we have to discuss the problem of evolution of quantum fields on GR background (inflaton evolution during inflation, axion field evolution etc). But GR isn't quantized as ...
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Variation of Gibbons-Hawking-York term. General boundary condition and total derivatives

It is actually a comment and question to the answer of Robert McNees in the following post: Explicit Variation of Gibbons-Hawking-York Boundary Term In deriving the variation of the extrinsic ...
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115 views

Resource for mass-charge interaction

My GR professor mentioned that trajectories of charged particles in GR are not the same as those of non-charged particles (i.e. charged particles don't move on geodesics). As I understood it, the ...
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193 views

I think I am misunderstanding Einstein's equivalence principle and his elevator

I'm having difficulties understanding why a gravitational acceleration can be guaranteed to be locally equivalent to an accelerating frame. Doesn't it matter on how the force is being applied? If the ...
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35 views

Distance of closest approach

When deriving the gravitational bending angle of light, In this paper, the author introduced $R$ (the distance of closest approach), in equation ($7$), to solve the problem. My question: How is $R$ ...
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90 views

Does isotropy imply homogeneity?

This question comes from exercise 27.1 in Gravitation by Misner, Thorne and Wheeler. They required the following: Use elementary thought experiments to show that isotropy of the universe implies ...
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2answers
131 views

What would a closed timelike curve look like?

What exactly are closed timelike curves. In a metric in which they would exist, what would they look like. What would it be like travelling through them? It obviously wouldn't look like a door. Would ...
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120 views

Variation of Christoffel symbol and Lie derivative

I've also asked this question on Math Overflow; I hope that asking in two separate fora is not a solecism. Under an infinitesimal diffeomorphism the Riemann metric changes by the Lie derivative $$ ...
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About spin 2, graviton, in the context of attractive force.

excerpt from Introduction to Black hole physics, Valeri P. Frolov and Andrei Zelnikov In this textbook, there is comment about spin of gravitons as follows For gravitating bodies the gravitational ...
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105 views

Relativity… Twin paradox

Sorry, but I have another stupid question about relativity. In the twin paradox: Let's say the travelling twin went to Proxima Centauri and back at 0,99c. However, he did not slow down to stop on ...
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What is the binding energy in General Relativity?

In general relativity, the potential energy is given by $$V(r)=\frac{h^{2}}{2r^{2}}\left(1-\frac{2M}{r}\right)-\frac{M}{r}.$$ Solving $V^{\prime}(r)=0$, there are two points where circular orbits ...
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The null geodesic for given geodesic [duplicate]

What is null geodesic equation for the static and spherically symmetric line element in $$ds^{2}=-K^{2}dt^{2}+\frac{dr^{2}}{K^{2}}+r^{2}(d\theta^{2}+\sin^{2}\theta{d\phi^{2}})$$ where ...
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61 views

What is the null geodesic equation? [duplicate]

What is null geodesic equation for the static and spherically symmetric line element in $$ds^{2}=-K^{2}dt^{2}+\frac{dr^{2}}{K^{2}}+r^{2}(d\theta^{2}+\sin^{2}\theta{d\phi^{2}})$$ where ...
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53 views

Relationship between gravitational time dilation and energy?

The rate that a stationary clock slows down near a massive object, relative to one far away, can be read off from the Schwartzschild metric: ...
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36 views

Tensor components multiplication vs. matrix multiplication [duplicate]

I'm teaching myself general relativity at the moment and I'm not sure I understand the difference between the product of tensor components and matrix multiplication. First of all, if $A$ is a $(2,0)$ ...
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58 views

How any trajectory can be linear?

From this article: An inertial coordinate system ought to be one in which free particles move in straight lines. But any trajectory may be stipulated to be rectilinear, and a coordinate system ...
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What is the radius of the event horizon?

I know that the Schwarzschild radius is given by $$r~=~\frac{2GM}{c^{2}}.\tag{1}$$ However, If we had the metric $$ds^2~=~−A(r,t)dt^2+\frac{dr^2}{B(r,t)}+r^2(dθ^2+\sin^2{θ}dϕ^2),\tag{2}$$ where ...
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How to derive the Schwarzschild radius? [duplicate]

I know that the Schwarzschild radius is given by $$r=\frac{2GM}{c^{2}}.$$ but I never seen a derivation for this equation. 1- Does anyone know how to derive this equation from general relativity? ...
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All of Physics! [duplicate]

In several of Neil Turok's talks, he talks about this equation that encompasses all of physics. Here it is: How much of it is true? If it isn't, then is it possible to put all of our knowledge of ...
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51 views

Physical motivation for mathematically extending solutions to Einstein's equations

Sorry if this question gets a little long; I want to explain why I'm asking it. The usual Schwarzchild metric $$ds^2 = -\left(1-\frac{2M}{r}\right) dt^2 + \left(1-\frac{2M}{r}\right)^{-1} dr^2 + ...
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The age of black holes

I have a very small understanding of space-time however I have been watching some interviews and reading articles featuring theoretical physicist Kip Thorne and I have a few questions that I hope can ...
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78 views

Will a black hole cause scattering of a gravity wave?

In my GR textbook, it states that gravity waves can undergo interference but not scattering. I am just starting the chapter on linearised gravity concepts (weak field approximation) and my apologies ...
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Non-local gravitational energy tensor

The well-known derivation of the Landau-Lifshitz gravitational energy pseudotensor, relies on several requirements: 1) that it be constructed entirely from the metric tensor 2) that it be index ...
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“Center of a black hole is a time”

$\newcommand{\d}[1]{\mathrm{d} #1}$In one lecture (around 1:33:15) of the series of lectures "Theoretical Minimum" of Prof. Susskind he talks about black holes and the Schwarzschild metric: $$\d ...
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Human max speed in open space

Suppose you are an astronaut forgotten in the middle of nowhere, between our solar system and proxima centauri's. Now, you are out of fuel. I heard that with some kind of movements, someone in free ...
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A classically charged point particle interacting with electromagnetism and gravity

Consider a classically charged point particle interacting with electromagnetism and gravity. The relevant dynamical variables are $\chi^\mu (\tau)$ of the particle, the electromangetic potential ...
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67 views

What is a “local” lorentz transformation of vielbein? How does it transform?

I'm struggling with Anthony Zee's chapter on differential forms in Einstein Gravity in a Nutshell, page 600. He asks us to prove that $$\omega= \Lambda \omega' \Lambda^{-1} - (d\Lambda) \Lambda^{-1}$$ ...
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Calculation of Einstein tensor for weak gravitational field

I am studying A First Course in General Relativity (2nd Ed.) by Bernard Schutz. I have some difficulty in deriving Eq.(8.32) on P.193, the form of Einstein tensor for weak gravitational field, which ...
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444 views

How much fuel is required for star travel considering relativistic time dilation?

John Rennie's Q&A How long would it take me to travel to a distant star? discusses about interstellar travel taking into consideration. There was a case that discussed about constant ...
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49 views

Which is the corrispondent of the Lorentz's transformation in general relativity?

The Lorentz's transformations tell us how space and time change in a flat case? There are a more general and powerfull transformation for general relativity?
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65 views

How and when are the relativistic corrections applied to GPS satellites?

It is known that there is a need to correct the onboard clocks to reduce the time difference from 38μs to 50ns. Where is relativity playing its role here? Why cant the clocks be simply synchronised ...
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85 views

The invariance vs constancy of the speed of light in vacuum

This is perhaps as much a question of semantics as of physics but it is something I have been thinking about recently and was wondering if anyone else had a perspective on this. Now, it could be that ...
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When space bends, what are the lines that are being bent?

In an electric field diagram, the lines represent the electrostatic force vector at the position. These lines are bent when you place a charge into the system. What is the equivalent description ...
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How is the Lagrangian defined in GR?

Reading about the Schwarzschild metric in general relativity I see that sometimes $$L=g_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}$$ and sometimes $$L=\sqrt{g_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}}.$$ Which is ...