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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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 ...
1
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1answer
83 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
136 views

Can energy bend space? [duplicate]

I know mass bends the space around it and I also remember matter can be converted into energy and vice versa, so my question is: can energy interact with space in a similar fashion as matter does?
0
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1answer
41 views

How to prove that the nonlinear completion of free massless spin-2 action must be Einstein-Hilbert action?

There is a saying that the nonlinear completion of free massless spin-2 action in Minkovski spacetime (that is Fierz-Pauli action) must be Einstein-Hilbert action up to Lovelock invariants. I find a ...
2
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1answer
67 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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2answers
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Is there a binary black hole system in the middle of the galaxy?

We have observed gravity effects from black holes in the center of galaxies, but galactic centers are dusty so we can’t tell if it’s one black hole or two black holes in a binary system in there. A ...
1
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1answer
29 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 ...
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0answers
46 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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4answers
231 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
70 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 ...
2
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2answers
102 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 ...
3
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1answer
103 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
83 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). ...
-1
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1answer
60 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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3answers
148 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 ...
1
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2answers
158 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 ...
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4answers
295 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 ...
0
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1answer
52 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 ...
3
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3answers
557 views

Theory that gets rid of dark matter/energy

Is there any physics theory that either groups together gravity and dark energy/dark matter or eliminates dark energy/dark matter by modifying standard understanding of gravity or any force? If so, ...
4
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6answers
1k views

What is the relation between General Relativity and Newtonian Mechanics?

What is the relationship of General Relativity and Newtonian Mechanics? Namely, which laws does GR replace of Newtonian Mechanics, and which laws of Newtonian Mechanics are incorporated into it. Or is ...
2
votes
1answer
87 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
37 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 ...
1
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3answers
153 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 ...
36
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15answers
16k views

Getting started self-studying general relativity

What are some good books, videos, websites for getting started with general relativity? I would prefer mathematically rigorous sources.
0
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2answers
136 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
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0answers
18 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 ...
11
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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 ...
3
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0answers
82 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 ...
0
votes
2answers
47 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
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1answer
53 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 ...
0
votes
1answer
68 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 ...
19
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4answers
3k views

Wormholes & Time Machines - for *experts* in GR/maths

EDIT: Further clarification in the context of answers/comments received to 20 Jan has been appended EDIT: 21 Jan - Response to the Lubos Expansion appended [in progress, not yet complete] EDIT: 23 ...
2
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0answers
168 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 ...
0
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2answers
119 views

How does the warping of time behave as a fourth dimension?

My problem is that I have a hard time grasping something if I can't conceptualize it, though maybe this can not be conceptualized, just accepted, in which case I thank you for your patience. The ...
2
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2answers
113 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 ...
0
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2answers
324 views

How do gravitons impact on general relativity?

As I'm reading about GR a lot lately, I was wondering: how do gravitons (if they exist ofc) impact the general relativity? Since in GR, when we look at particles moving in space-time, we are only ...
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0answers
96 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 ...
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2answers
122 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
45 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 ...
-1
votes
4answers
231 views

Could a photon travel faster than the speed of light in vacuum?

If the cosmic speed limit is the speed of light in vacuum, then what happens when a photon traveling through space meets gravity? Wouldn't gravity pull on the photon that's already traveling at max ...
0
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0answers
22 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 ...
1
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1answer
93 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 ...
9
votes
2answers
537 views

The Aharonov-Bohm effect is purely classical, right?

Every discussion I've ever seen of the Aharonov-Bohm effect makes a big deal of its being a quantum effect with no classical analogue. But as far as I can tell it is present already at the classical ...
0
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0answers
18 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 ...
0
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1answer
77 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
votes
2answers
69 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 ...
4
votes
2answers
254 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 ...
2
votes
2answers
451 views

Finding the metric tensor from the Einstein field equation?

I have have set my self a challenge to learn all the maths behind the Einstein field equation (EFE), and from reading it seems that the Metric tensor is the thing we are trying to find (from the 10 ...
8
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3answers
170 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 ...
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1answer
68 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} ...