A theory that describes how matter produces and responds to 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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A ball in the gravity potential field of a black hole — seems a paradox

As illustrated in the following diagram (A, B, C, D are 4 specified space points, and C is close to a black hole), a small ball at distance of a black hole is stationary (suppose now it's mass is m0) ...
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0answers
46 views

Friedmann Equations Derivation [closed]

I was trying to understand how one goes from the following system of Friedmann equations \begin{cases} \frac{\dot{a}^2}{a^2}+\frac{k}{a^2} = \frac{8\pi\rho(t)}{3} + \frac{\Lambda}{3}\\ ...
2
votes
1answer
63 views

Heuristics for the Hawking mass

I have the following definition of Hawking Mass. Given a spacelike 2-surface $S$ embedded in a 3+1-dimensional Lorentzian Manifold $L$, $$ M(S) := \sqrt{ \frac{\text{Area}(S)}{16 \pi}} \left(1- \frac ...
2
votes
1answer
58 views

Non-linearity and self-coupling of gravity

I have heard that non-linearity of Einstein's field equations has to do with the fact that gravity self-couples. What does non-linearity have to do with self-coupling?
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4answers
2k views

Will an object always fall at an infinite speed in a black hole?

Most of you if not everybody will agree that the stronger the gravitational pull, the faster an object will fall. For example, on a planet with 50 times the gravity of Earth, any object will hit the ...
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0answers
36 views

How one can solve Friedman equations of General relativity numerically?

How one can solve Friedman equations numerically subjected to any initial condition?
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1answer
25 views

Black holes in a denser media

In Crown Glass, the speed of light is 1.52 times the speed of light in vacuum. Consider the following hypothetical situation: Hypothetical Situation If a black hole is surrounded by a giant crown ...
2
votes
4answers
97 views

Normal Vectors to these Hypersurfaces on a Lorentzian Manifold

With respect to the coordinates $(x^{0},x^{1},x^{2},x^{3})=(v,r,\theta,\phi)$, we have the following components of the metric tensor: $\begin{bmatrix} g_{00} & g_{01} & g_{02} & ...
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1answer
49 views

Bianchi Identity using null tetrad

I'm currently looking at the Newman-Penrose Formalism, and trying to understand where there sets of equations come from. For that, I need to know how I can write the second Bianchi identity for the ...
5
votes
3answers
86 views

Has anyone tried Michaelson-Morley in an accelerated frame?

After doing much more digging than I thought I had to do, I found out that the speed of light is NOT invariant in an accelerated reference frame. Has anyone done any experiments to confirm this? In ...
39
votes
8answers
3k views

In theory, could gravitational waves be used to make a “gravity laser”?

The sources I've read compare gravitational waves to electromagnetic waves. I'm curious to what extent this is. In theory, could gravity be harnessed in similar ways to how we've used electromagnetic ...
1
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0answers
47 views

Who created the energy conditions? [migrated]

The earliest text I've been able to find that explain the GR energy conditions is "The large scale structure of space-time" (1973) by Hawking and Ellis. However in Barcelo and Visser's paper ...
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1answer
48 views

Relativity of simultaneity in Galileo's Leaning Tower of Pisa experiment

Galileo's conclusion can be roughly summed up as: objects of different masses, when dropped from the same height, descend in the same time interval, independent on their masses (neglecting friction). ...
3
votes
2answers
89 views

General Relativity view of Newton's apple

If one considers the free fall of an object of mass $m$ from a hight $h$ in the Earth's gravitational field (neglecting air friction) from the point of view of GR, what would be the main corrections ...
0
votes
1answer
41 views

Weyl scalar calculation

I'm trying to compute Weyl scalars, but don't really understand the formulae for them, in the sense I don't understand how to compute them. Let's take ...
0
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1answer
41 views

Where do we get the terms involving $\Phi$ in parentheses come from in the static weak field metric?

I am confused about the static weak field metric. As written in Hartle, it reads \begin{equation} ds^2 =-\left(1+\frac{2\Phi(x^i)}{c^2}\right)(cdt)^2 +\left(1-\frac{2\Phi(x^i)}{c^2}\right)(dx^2+dy^2 ...
2
votes
4answers
157 views

Kerr metric Christoffel symbols

I've been slaving away trying to calculate the Christoffel symbols for the Kerr metric. Does anybody know of a link that I could compare my answers to? I've done some Google searches and all I can ...
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2answers
72 views

Black hole area theorem and Hawking radiation

Black hole area theorem states that surface area of a black hole does not decrease with time (see page 10 of Introductory Lectures on Black Hole Thermodynamics, Ted Jacobson ...
0
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3answers
116 views

If we're holding hands, and you're inside the event horizon of a black hole, do we both fall in?

Imagine some science fiction scenario where two people are floating through space holding hands orbiting a black hole. If one person falls close enough to the black hole that they're within the event ...
3
votes
1answer
83 views

Curvature of Light around a Black Hole [duplicate]

I am in a computer graphics class at my university and for my final project, I have chosen to create a program which renders a simple non-rotating black hole and models the curvature of light around ...
1
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1answer
73 views

Transpose of (1,1) tensor

When we transpose a (1,1) tensor, shall we simply switch the two indices while keeping their upper/lower positions or switch them and also switch their upper/lower positions? In general, would the ...
0
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0answers
34 views

Correct calculation for a quantum black hole (example: LHC)?

What is the right equation to calculate a quantum black hole? As an example I like to take the figures from LHC. http://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/beam.htm Top Energy ...
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0answers
36 views

What level of mathematics would I need to understand the physics of a black hole? [duplicate]

I recently went to go see Interstellar and was awed by the visualizations of the wormhole and the black hole Gargantua. I read that noted physicist Kip Thorne was a consulting producer on the film. I ...
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0answers
17 views

Does a time-evolving gravitational field or potential have any important/interesting effects?

I have learned from classical electromagnetism that a time-evolving magnetic field gives rise to a contribution to an electric field, and vice-versa. Do gravitational fields have an analogous effect ...
3
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0answers
70 views

Can I hide a charge behind a black hole?

Suppose that you are standing on one side of a black hole. I'm standing directly opposite you, on the other side of the BH, and I'm holding a charged particle. Is it possible for us to be positioned ...
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votes
3answers
1k views

How many times can light revolve around a black hole?

Take a light ray approaching a black hole from infinity which goes out again to infinity. What is the maximum finite rotation it can describe? (I know it can loop around indefinitely in the ...
0
votes
2answers
122 views

Speed of light constant for all observers [duplicate]

General relativity has been proven many times over to be correct. In my meager understanding of things, they are all premised on the fact that the speed of light is constant to all observers. I would ...
0
votes
2answers
43 views

Is the influence of gravity greater than light? [duplicate]

As the influence of gravity is infinite throughout the universe.is the influence of its force on a body very far away faster than the speed of light.suppose a star dies...is the influence of its ...
0
votes
1answer
56 views

Definition of the Lagrangian for a relativistic point particle in curved space

I have read that the Lagrangian in GR is defined as $L=\frac{\mathrm{d}s}{\mathrm{d}u}$, where $\mathrm{d}s = g_{ab}\mathrm{d}x^a\mathrm{d}x^b$ is the line element with the metric tensor $g_ab$ and ...
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vote
3answers
138 views

Determining whether a space is really three or two dimensional? [closed]

A space purports to be three dimensional with the metric $$dl^2=dx^2+dy^2+dz^2-\left(\frac{3}{13}dx+\frac{4}{13}dy+\frac{12}{13}dz\right)^2$$ How can I show that it actually represents a two ...
2
votes
0answers
66 views

Covariant versus “ordinary” divergence theorem

Let $M$ be an oriented $m$-dimensional manifold with boundary. As stated in Harvey Reall's general relativity notes (here) or Sean Carroll's book, the "covariant" divergence theorem (i.e. with ...
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votes
3answers
57 views

Need of Fourth Time dimension

What is the need of 4th dimension in GR. Can we solve the problem without assuming 4th dimension. If we specify in three dimensional grid values of relative time in all the elements of grid, can we ...
2
votes
2answers
140 views

Is the universe 5 dimensional space-time or 4?

we've been told that in General Relativity (GR), matter tells space how to curve and space tells matter how to move. But my question is, if 3 dimensional space was curved by matter then it should be ...
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0answers
94 views

What does it mean when it is said that “General Relativity and Quantum Mechanics are incompatible”? [duplicate]

In many of the pop-science-y documentaries on theoretical physics I often hear the statement: "General Relativity and Quantum Mechanics are incompatible" Some googling tells me that "General ...
2
votes
5answers
311 views

Where does General Relativity (GR) fail experimentally? Experimental shortcomings of GR?

When speaking with researchers and professors at my physics department, I sometime catch this undertone in the conversation when speaking about GR: almost as if some are not entirely convinced about ...
1
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1answer
71 views

How physical are vacuum solutions to Einstein's equations?

It is shown in any standard textbook on general relativity how you might get black holes and gravitational radiation, both of which are vacuum solutions to field equations, i.e., such that ...
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votes
1answer
46 views

Hawking radiation and charge

If black hole has a charge, they will lose charge due to Hawking radiation. If black hole has positive charge, it emit more positron than electron. And the same argument I can apply in rotating black ...
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votes
0answers
32 views

Charged black hole

It is known that there is solution of Einstein's equations for charged black hole. Reissner–Nordström metric in case of non-rotating charged black hole and for rotating charged black hole is a ...
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vote
2answers
87 views

How can gravitions exist without violating GR? [duplicate]

How can gravitions exist without violating GR, since GR says that gravity is curvature in space-time.
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0answers
19 views

Do photons exert gravity? [duplicate]

I read about GR today and came across the Bonnor beam. As I understand it, two parallel light beams (in a flat space) will in fact creep – slowly – towards each other. As Wikipedia puts it: On the ...
2
votes
1answer
71 views

Eternal black holes and Hawking radiation

I have a fairly simple question which is confusing me a lot. As Hawking showed, a black hole originated by collapse will emit Hawking radiation. This process will reduce the mass of the black hole ...
1
vote
1answer
81 views

How can I use Einstein's field equations? [duplicate]

Every time I try to find the answer to this question I get redirected to different pages that ultimately do not end up answering my question. I have some understanding of Riemannian geometry but have ...
6
votes
2answers
820 views

Why is it hard to detect a black hole

I've read in some texts that we can't directly observe a black hole in space because not even light can escape from its gravity. Some of the indirect observational methods mentioned are, gravitational ...
4
votes
2answers
163 views

Can gravitational waves escape from inside of black holes? [duplicate]

I understand that light cannot escape from inside of an event horizon because the spacetime curvature is too warped for photons to escape. On the other hand, gravitational waves are ripples of ...
0
votes
2answers
56 views

Proving a relation with Four-velocity tensor [duplicate]

I'm trying to show that: $U^a_{\space\space;b}U^bU_a = 0$ (Where U is four-velocity) and I'm stuck on how to go about it. I tried expanding it out into the Christoffel symbols, but that didn't seem ...
0
votes
1answer
67 views

Effect of a rotating disk on a grandfather clock

The question is as follows: A grandfather clock is placed on a rotating disk. Given the disk rotates once every minute, how long does it take for the clock to be one second out? Am I correct in ...
0
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0answers
17 views

Schwarzschild radius after inflation [duplicate]

Update and refinement of previous question. At the beginning (Big Bang) if there was parhaps a singlarity as such GR, Quantum theory breaks down and we do not really know what happens. that's why I ...
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1answer
62 views

Does anyone recognize the line element $ds^2 = ( 1 - \frac{2m}{r} )dt^2 + 2 dt dr$?

I've stumbled upon the line element $ds^2 = ( 1 - \frac{2m}{r} )dt^2 + 2 dt dr$. Obviously the corresponding metric tensor has components: $\begin{bmatrix} g_{tt} & g_{tr} \\ g_{rt} & g_{rr} ...
2
votes
2answers
84 views

Proper length in GR

What meaning/use is associated with the notion of proper length in general relativity? Do you know an example of any quantity that depends on it? I have so far found statements like "the length ...
8
votes
3answers
145 views

Why doesn't $ds^2 = 0$ imply two distinct points $p$ and $p'$ on a manifold are the same point?

Let's suppose I have a spacetime manifold $M$. Let $p$ be a point on my manifold. Now I move from $p$ to some other point $p'$. Presumably I should have moved some "distance" right? How can I speak of ...