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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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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35 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
57 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 ...
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1answer
73 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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1answer
159 views

Higher-Dimensional Metrics in (Hyper)-Spherical Coordinates

I want to compute the components of the Riemann curvature tensor (for a case similar to the Schwarzschild solution) in 4 + 1 dimensions, but I want to use a higher-dimensional analogue of spherical ...
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1answer
437 views

How does the Hubble parameter change with the age of the universe?

How does the Hubble parameter change with the age of the universe? This question was posted recently, and I had almost finished writing an answer when the question was deleted. Since it's a shame to ...
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2answers
123 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 ...
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1answer
99 views

Maximum aging and path of rock

When a rock falls from a ledge, why does it head to the surface and not up to where time runs faster? If a rock, free from forces, follows a worldline of maximum aging, why would that rock approach ...
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3answers
705 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, ...
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2answers
91 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. ...
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1answer
123 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 ...
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2answers
297 views

Differential geometry of Lie groups

In Weinberg's Classical Solutions of Quantum Field Theory, he states whilst introducing homotopy that groups, such as $SU(2)$, may be endowed with the structure of a smooth manifold after which they ...
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2answers
114 views

Uniqueness or multiplicity of ADM masses for spacetime manifolds with more than one “end”?

The question is: What is the mathematical and/or physical basis for saying that a (static) spacetime manifold with more than one asymptotically flat region at infinity ("end") has a distinct ...
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0answers
56 views

What are Galileons good for?

Lately I've seen many papers on types of field theories known as Galileons, and I'm wondering what the motivation for studying them is. I often hear of them in the context of "well-behaved" IR ...
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8answers
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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
414 views

Maxwell's equations in curved spacetime

I know that we can write Maxwell's equations in the covariant form, and this covariant form can be considered as a generalization of these equations in curved spacetime if we replace ordinary ...
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5answers
132 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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1answer
68 views

$SO(p,1)$ transformation on black p-branes

I'm working on Blackfolds at the moment and I'm trying to boost-rotate( $SO(1,p)$ ) the p-brane $$ds^2=ds^2_{Sch}+\sum_{i=1}^p dz_i^2$$ Where $ds^2_{Sch}$ is the Schwarzschild metric in $N$ ...
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2answers
103 views

Can we add two singularities and make a single singularity?

My question is if we have two black hole and they will merge into each other, then where will be the singularity?
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4answers
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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 ...
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1answer
184 views

Wave Packet in Curved Spacetime

It is known that the classical equation of motion for a scalar field wave packet on a curved spacetime background gives the geodesic trajectory (the e.o.m. is $(\nabla_\mu \nabla^\mu + m^2) \Phi=0$). ...
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1answer
62 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 ...
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1answer
87 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
170 views

Einsteins gravity Space time

I'm having a difficulty in understanding Einstein's version of gravity as "space time curvature" (I could be a total physics idiot, please point out !). How does an object on the surface of earth ...
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1answer
31 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 ...
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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}\\ ...
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1answer
57 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 ...
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1answer
24 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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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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4answers
94 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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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 ...
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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 ...
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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 ...
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1answer
94 views

If a point r lies in the boundary of the chronological future of another point p, why does the chronological future of r belong to that of p?

I am studying the global causality of the spacetime. Here, I come across a problem. Suppose a point $r\in \partial I^+(p)$. $I^+(p)$ is the chronological future of a different point $p$ in ...
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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 ...
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1answer
47 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). ...
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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 ...
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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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3answers
115 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 ...
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2answers
69 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
154 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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1answer
39 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 ...
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3answers
474 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, ...
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6answers
790 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 ...
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3answers
53 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 ...
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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 ...
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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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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 ...
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17answers
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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.