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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Lapse and shift in ADM decomposition

Poisson in Relativist's Toolkit and also other authors in various papers state explicitly that after one does the 3+1 decomposition, the lapse and shift $N$ and $N^a$ are non-dynamical variables, and ...
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0answers
47 views

Connection one-form and suppressed indices

I am reading Sean Carroll's notes on GR, which states (Page 91): Using our freedom to suppress indices on differential forms, we can write the defining relations for these two tensors as: $$ T^a ...
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0answers
21 views

Calculate Total Energy Of Universe [duplicate]

Physicist using $mc^2$ to calculate positive energy and $-MmG/R$ to calculate negative energy to calculate total nergy of the universe but I heard that one of them is relativly invariant and other ...
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1answer
36 views

Basic question about curved and flat indices, and the Dirac matrices on $S^5$

In discussing the Kaluza-Klein formalism for Type IIB Supergravity on $S^5$, or the AdS5xS5 compactification, one requires Killing spinors on $S^5$. I read that the Dirac matrices on $S^5$ satisfy ...
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36 views

Does the rotation of the Earth affect time?

If the Earth were to spin from east to west instead of west to east, how would that affect time or our perception of it?
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1answer
78 views

Study the center and interior of a black hole using quantum entanglement

Having just watched the latest in a long line of space movies; Interstellar tries to combat the problem of studying the center of a black hole and understanding what's going on inside. My question is, ...
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2answers
72 views

Allowable spacetime deformations [closed]

What deformations are possible with spacetime? By 'deformation' I am referring to the kind of change in spacetime caused by the presence of a mass which deforms spacetime sufficiently to deflect ...
7
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3answers
182 views

Can the Unruh effect be confirmed by the LHC?

Two short questions regarding the Unruh effect. There are related answers on this forum and on wikipedia, but I am looking for confirmation of my own intuitive assumptions, so a straightfoward yes or ...
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0answers
38 views

Light rays in linearized General Relativity

In General Relativity, particles follow geodesics in space-time, obeying $$\ddot x^a + \Gamma^a_{bc}\dot x^b\dot x^c=0,$$ where $\Gamma^a_{bc}$ are the Christoffel symbols, expressed in terms of the ...
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1answer
36 views

What observation(s)--if any--confirm that the types & concentrations of energy, which are influenced by gravity, are the same ones that cause gravity?

General relativity allows various forms of energy to participate in the gravitational force. What observation(s)--if any--confirm general relativity's notion that the various types & ...
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1answer
61 views

Real-world evidence that non-massive entities (or even: antiparticles), and their behaviors, are sources of gravity?

The theory of general relativity tells us that non-massive entities, and their behaviors, are possible sources of gravity. Mass isn't needed, the theory says. What's the real-world evidence that ...
2
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1answer
80 views

Does spacetime have symmetric curvature around an object? If yes, then why do planets revolve around the Sun in elliptical orbits?

Does spacetime have symmetric curvature around an object? If yes, then why do planets revolve around the Sun in elliptical (as opposed to circular) orbits?
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2answers
144 views

How confident are we that mass is not being lost in the universe?

After reading about the latest super-massive black hole in Nature 518, 512–515 (26 February 2015), I couldn't help but wonder if the accelerating expansion is a result of mass being lost. Would a ...
4
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2answers
134 views

Why are orbits around black holes stable?

Black hole theory involves space (or space-time), itself, being sucked into the black-hole, with the event horizon marking the point at which space/space-time is moving faster than the speed of light. ...
6
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0answers
223 views

What are Galileons good for?

Lately I've seen many papers (for example "The galileon as a local modification of gravity"; 292 total hits on the arXiv) on types of field theories known as Galileons, and I'm wondering what the ...
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1answer
142 views

Gravity in $d$ spacetime dimensions

Given the following action $$S=\frac{1}{16\pi G}\int d^4x \sqrt {-g}(R+aR^2+bR_{\mu\nu}R^{\mu\nu}+cR_{\mu\nu\lambda\sigma}R^{\mu\nu\lambda\sigma}),$$ which is in 4D. How to we generalise this ...
2
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1answer
91 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?
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3answers
766 views

Gödel's solutions to Einstein's relativity equations and their consequences

Gödel gave certain solutions to Einstein's relativity equations that involved a rotating universe or something unusual like that; that predicted stable wormholes could exist and therefore time travel, ...
0
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1answer
34 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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5answers
151 views

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
54 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
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1answer
67 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
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1answer
64 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
39 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
26 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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4answers
150 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
60 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
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3answers
90 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 ...
40
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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 ...
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1answer
54 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). ...
2
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2answers
94 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 ...
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1answer
46 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
46 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
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4answers
194 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
91 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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3answers
128 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
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1answer
85 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
vote
1answer
78 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 ...
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0answers
35 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
37 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
74 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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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
124 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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2answers
44 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
60 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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3answers
140 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
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0answers
83 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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3answers
73 views

Need of Fourth Time dimension [closed]

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 ...