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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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 ...
3
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3answers
186 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 ...
0
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1answer
29 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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1answer
70 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
118 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 ...
2
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1answer
93 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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44 views

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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1answer
104 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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2answers
80 views

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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0answers
20 views

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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0answers
57 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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1answer
51 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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2answers
57 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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3answers
820 views

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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3answers
144 views

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? ...
3
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1answer
116 views

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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49 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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1answer
72 views

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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0answers
74 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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0answers
49 views

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 ...
4
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4answers
370 views

“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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2answers
49 views

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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76 views

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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1answer
58 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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2answers
111 views

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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3answers
439 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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47 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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2answers
47 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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2answers
80 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 ...
2
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4answers
816 views

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 ...
5
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1answer
106 views

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 ...
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1answer
44 views

Distance and luminosity distance

In my cosmology lecture notes I read that a way to measure distances in cosmology is to use standard candles and the comparison between "absolute luminosity" of the candle and the apparent luminosity. ...
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32 views

Differential precession due to gravitational waves

To motivate the question, Andy Strominger recently put out a paper on calculating the Sagnac shift of counterrotating beams due to the angular momentum flux of a passing gravitational wave. See ...
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50 views

Nabla or semicolon notation for covariant derivative? [closed]

$$A_{\,;\alpha}^{\mu}=\nabla_{\alpha}A^{\mu}$$ Are there any pros and cons regarding these two notations for denoting the covariant derivative?
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1answer
46 views

Derivation of form of perfect fluid stress-energy tensor

Given the perfect fluid equation: $$T_{\mu\nu}=(\rho+p)U_\mu U_\nu+pg_{\mu\nu}$$ How does one derive the following form? $$T_\mu^\nu=\mbox{diag}(-\rho,p,p,p)$$ I understand one needs to raise an index ...
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1answer
61 views

What is the metric of a constant electromagnetic (pure electric or pure magnetic) field?

For example, imagine a magnetic field $B_x$ directing in $\hat{x}$ direction filling all the space. What is its associated metric field? I can construct the electromagnetic stress-energy tensor for ...
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2answers
134 views

The Big Bang theory hypothesis

Is there a simple way to state the hypotheses of the Big Bang theory? I have the impression that the Big Bang singularity is merely a consequence of Freedman equations. Could somebody clarify what ...
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1answer
53 views

Does gravity slow entropy? [closed]

Just got to thinking about why time slows in a gravitational field. It occurred to me that, in a gravitational field, the closer you get to the source the slower time seems to travel. But also, the ...
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0answers
31 views

Zero mean curvature and maximal volume

I have a 1+1 asympotically flat spacetime system (spherical symmetry) for which I'm trying to find the hypersurface which maximizes the volume enclosed in a sphere of a given radius $r=R$. **It seems ...
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0answers
31 views

Do anyone know a good software that where I can easily find the metric from the stress-energy tensor? [duplicate]

I'm using SageMath but the obtainment of the metric from the stress-energy tensor is not trivial, i.e., it is not implemented in a predefined function. Do anyone know a good software that where I can ...
2
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2answers
224 views

Why is the metric tensor symmetric? [duplicate]

I was reading Schutz, A First Course in General Relativity. On page 9, he argued that the metric tensor is symmetric: $$ ds^2~=~\sum_{\alpha,\beta}\eta_{\alpha\beta} ~dx^{\alpha}~dx^{\beta} $$ ...
-1
votes
1answer
35 views

modified gravitational model

In the modified gravitational model $ f(R)=R+\lambda{R_{0}}\left(\left(1+\frac{R^{2}}{R_{0}^{2}}\right)^{-n}-1\right) $ what are the units of $\lambda$ and $R_{0}$.
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1answer
63 views

Difference of connections in the Killing vector equation

For the Killing vector equation, I sometimes see it written in terms of spin connection $\omega$ and other times in terms of the affine connection $\Gamma$. More clearly ...
0
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1answer
53 views

Circular orbits in general relativity(GR)

Reading about Schwarzschild geodesics, I found that circular orbits are possible when the effective force $$ F=-\frac{dV}{dr}=-\frac{\mu{c^{2}}}{2r^{4}}\left(r_{s}r^{2}-2a^{2}r+3r_{s}a^{2}\right)=0 ...
1
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1answer
74 views

What is the partial differential equation expansion of the Einstein Field Equations?

I have read that the Einstein Field Equations (http://en.wikipedia.org/wiki/Einstein_field_equations) can be expressed as a series of differential equations. Some say 16, others say 10 (The disparity ...
2
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1answer
345 views

What happens to the total volume of a chunk of space that is being sucked into a black hole?

Does it increased, decrease, or stay the same? Maybe it explodes to infinity... Here is a similar question: Do black holes have infinite areas and volumes? But it's different because it asks how to ...
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28 views

How does one show that asymptotically $AdS_3$ spacetimes are locally $AdS_3$?

Time and again I keep reading that any asymptotic $AdS_3$ spacetime is locally isomorphic to $AdS_3$. I tried to find proof of this by analyzing the Riemann tensor $R_{\rho\sigma\mu\nu} $ in Ricci ...
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2answers
286 views

How can we feel the effects of a Black Hole if all the mass is gone?

This question may help me learn more about the subtleties involved between the notions of gravity, in the Newtonian sense and those of curved spacetime, in the General Relativity sense. I will take ...
8
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1answer
250 views

Is John Nash's “Interesting Equation” really interesting?

As recently mentioned in the news, before his passing, John Nash worked on general relativity. According to the linked article John Nash's work is available online from his webpage. His work is ...