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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What do physicists mean by ${g^{i}}_j$?

Maybe this is an idiot question, but in relativity I see a lot of ${g^{i}}_j$ for a metric tensor $g$. Is this just $$\delta^i_j ~=~ g(dx^i \sharp, \partial_{ x^j})~?$$
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1answer
204 views

Detailing why a scalar gravity theory predicts no bending of light [closed]

I want to understand in technical detail why a particular scalar theory for gravity predicts no bending of light. It is left as a question, either in "Gravitation" by Misner, Thorne, and Wheeler, ...
4
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1answer
89 views

Metric of a manifold foliated by maximally symmetric submanifold

I am reading the last chapter (Schwarzchild solution and Black Holes) of Sean Caroll's GR notes (http://arxiv.org/abs/gr-qc/9712019). While talking about spherical symmetry, he says how the ...
5
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1answer
487 views

How to find the Stress-Energy tensor?

I am a bit at loss about how to proceed to find the stress-energy tensor given some distribution of matter. The Wikipedia page gives some examples, and some (inequivalent) definitions for it: Using ...
2
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1answer
337 views

Does time expand with space? (or contract)

Einstein's big revelation was that time and space are inseparable components of the same fabric. Physical observation tells us that distant galaxies are moving away from us at an accelerated rate, and ...
2
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2answers
242 views

Accounting for metric tensor derivatives in Einstein-Hilbert action

I'm puzzling over the canonical derivation of GR from the Einstein-Hilbert action; getting the derivation to gel with an explicit treatment of the functional derivative isn't working out. So the ...
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1answer
199 views

Conserved quantity along geodesic

In my general relativity textbook (Carroll), he says that "the geodesic equation (together with metric compatibility) implies that the quantity $\epsilon ...
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2answers
166 views

What if a particle falls into the center of a central field? [closed]

Given a central field $U(r)$ satisfies $U(r) \rightarrow -\infty$ when $r \rightarrow 0$, then What if a particle falls into the center of a central field? Can you help me analysis this question in ...
7
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1answer
153 views

does the beam of a laser have 'throw'?

I was thinking about Einstein's train and platform experiment and was wondering if a beam of light experiences throw? Let me explain, if I take a water hose and point it straight out and then swing ...
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5answers
1k views

Does antimatter curve spacetime in the opposite direction as matter?

According to the Dirac equation, antimatter is the negative energy solution to the following relation: $$E^2 = p^2 c^2 + m^2 c^4.$$ And according to general relativity, the Einstein tensor (which ...
3
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1answer
291 views

What exactly is the connection between the Jacobi and Bianchi identities

While reviewing some basic field theory, I once again encountered the Bianchi identity (in the context of electromagnetism). It can be written as $$\partial_{[\lambda}\partial_{[\mu}A_{\nu]]}=0$$ ...
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2answers
258 views

Watching something fall into a black hole from far away

I am observing (theoretically) an object falling into a black hole from a safe distance away. My understanding is that from far away it appears as if the body will asymptotically approach the event ...
3
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1answer
188 views

Photon “stuck” on the event horizon of a black hole

According to what I've read on special relativity, $c$ is the speed limit for every object in the universe, and according to Einstein, an object's speed through the three spatial dimensions plus its ...
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0answers
108 views

Euclidean black hole extrinsic curvature

I have read that the extrinsic curvature at the horizon of a euclidean black hole is zero? Does anybody know how this can be shown?
2
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0answers
60 views

Gravity and Larmor effect

I have a Q: Does "Equivalent Principle" and "Larmor effect" imply that the charged particle should radiate electromagnetic wave if it is at rest in uniform gravitational field (like it is at rest on ...
2
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1answer
128 views

Is self gravitation theoretically impossible?

Is it theoretically possible to create some system such that the energy distribution creates a gravitational potential offset from its center of mass (or energy?) so that the body continually 'falls' ...
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4k views

Does someone falling into a black hole see the end of the universe?

This question was prompted by Can matter really fall through an event horizon?. Notoriously, if you calculate the Schwarzschild coordinate time for anything, matter or light, to reach the event ...
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1answer
244 views

How does time relate to mass and velocity

I understand that the larger the mass the greater gravity is and the slower time is, as well the faster an object is traveling the slower time passes. My question is that since the faster an object ...
6
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1answer
124 views

Could dark energy make a large black hole less black?

Theoretically, if a black hole grew to a huge scale such that the effect of dark energy was large, could the black hole become 'normal' space again (i.e. no horizon or singularity)? What I'm trying ...
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1answer
133 views

Different age of universe

According to general relativity time runs slowly near a massive body. So, I have a question bothering me from some time, that if time for every body/object in universe runs at a different rate, then ...
2
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3answers
255 views

Does GR imply a fundamental difference between gravitational and non-gravitational acceleration?

Does the equivalence principle imply that there is some fundamental difference between acceleration due to gravity and acceleration by other means (because there is no way to 'feel' free fall ...
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1answer
72 views

Why are trajectories in General Relativity speed-dependant?

I'm a secondary student who never studied any general relativity level maths (yet!), but I heard that in general relativity objects with mass and energy deform space-time, and therefore bodies move in ...
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1answer
55 views

LC Oscillator and relativity

There are two identical LC oscillators with electronic counters attached indicating how many times they have oscillated (from the time they are turned on). They are turned on simultaneously and one is ...
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2answers
152 views

Variance in speed of light

While discussing this question (Does light have an unending journey?) I stumbled on the fact that light's speed is constant only in inertial frame. What I happened to do was add up the expansion of ...
2
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1answer
451 views

Deriving an equation involving Killing vectors

I'm currently studying Carroll's GR book Spacetime & Geometry, and ran into some trouble understanding the text. When discussing Killing vectors, Carroll mentions that one can derive ...
2
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0answers
234 views

what are the direct real life applications of general relativity and quantum physics [closed]

What are the direct real life applications of general relativity other than nuclear technology? What I meant was, was there any technology developed based on general relativity that can benefit ...
2
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1answer
79 views

Why is general relativity only formulated in continuum terms?

So, when we are discussing Newtonian mechanics, we treat particles as point particles. In continuum mechanics, which I understand to be a version in which mass is continuously distributed, we have ...
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1answer
401 views

Asymptotic symmetry algebra

So after a lot of research, and tons and tons of papers that I've went through, I finally have some idea how to solve the equations that will give me candidates for the asymptotic symmetry group for ...
4
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1answer
124 views

Does a diatomic molecule falling into a black hole dissociate?

I've just answered Dipping a Dyson Ring below the event horizon, and while I'm confident my answer is correct I'm less certain about the exact consequences. To simplify the situation consider a ...
4
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1answer
113 views

Trajectories of particles with spin in Einstein-Cartan theory

The Einstein-Cartan theory is a generalisation of General Relativity insofar as the condition that the metric affine connection is torsion-free is dropped. In other words, the space time is a ...
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1answer
246 views

Does a black hole have an interior or does the spacetime manifold itself end at the event horizon? [closed]

There have been a number of intriguing ideas over the years hinting at the possibility that a black hole might not have an inside, that it might consist of nothing but a surface and an external ...
3
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1answer
68 views

What is the correct form of the NHEK metric?

I've noticed that in different articles people are writing the near horizon extreme Kerr metric (NHEK) in different forms. Original Kerr/CFT correspondence article by Guica et. al. follows ...
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1answer
523 views

General Relativity: Christoffel symbol identity

I want to show that $$\Gamma ^{\mu}_{\mu \nu}=\partial _\nu (\ln \sqrt{|g|}) .$$ (Here $|g|$ denotes the determinant of the metric.) Working out the left hand side:\begin{align} \Gamma ^{\mu}_{\mu ...
6
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1answer
317 views

Diffeomorphism Invariance of General Relativity

I'm sorry I know this has been asked before, but I'm still a bit confused. I understand that an active diffeomorphism $\varphi:M\to M$ can be equivalently viewed as a coordinate transformation so that ...
0
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2answers
444 views

General relativity: Induced metric and Killing vector fields

Assume that in spacetime ($M,g_{ab}$) there is a hypersurface generated by a set of independent one-parameter transformations acting on one single point, the generators of these transformations being ...
0
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1answer
130 views

Stress-energy tensor. Why this general form?

How is the stress energy tensor obtained? In most textbooks, it's simply stated as $$T^\mu{}_\nu=(\rho+P)U^\mu U_\nu-P\delta^\mu{}_\nu$$ I can see why this makes sense for a comoving observer at ...
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1answer
33 views

Flat space current conservation sign confusion

It is said that in Minkowski spacetime, the current conservation law for the number current $N^\mu$ where $N^0$ is the number density and $N^i, i=1,2,3$ is the particle flux in the $x^i $ direction, ...
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0answers
85 views

Interpretation of contribution of gravitational potential energy to the gravitational field

In terms of General relativity we have as a matter of principle that anything that has inertial mass contributes to gravity. All forms of potential energy have inertial mass, it follows that the ...
4
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1answer
193 views

When one discusses the “boundary” of Anti-de Sitter space, what do they mean precisely?

The AdS/CFT correspondence refers to the "boundary" of AdS space but I'm a little confused about what this means. Typically, one writes the AdS metric in the form $ds^2= \frac{L^2}{z^2}(-dt^2+d\vec ...
2
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3answers
259 views

How accurate is Newtonian Gravity?

I know that really fast moving things need Relativity rather than Newtonian physics. I also know the quirk of the Mercury´s orbit. But just how much more accurate is General Relativity than Newton´s ...
5
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1answer
173 views

Given finite speed of gravity, why didn't Earth fell into the Sun already?

When Sun and Earth are moving, at each moment $t$ they are attracted not to the current position of each other, but to the position of each other at $t-\Delta t$, where $\Delta t$ is the time required ...
2
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1answer
190 views

Christoffel symbols and Dirac matrices mathematical similarities?

Maybe mine is a silly question, but are there mathematical similarities or common roots between the Christoffel symbols: $ \nabla - \partial = \Gamma $ and the Dirac matrices $ ( \gamma^\mu ...
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3answers
3k views

Are Stephen Crothers' claims legitimate? [closed]

I came up last night with a talk given by Stephen J. Crothers in which he claims that black holes and the Big Bang have no basis in general relativity. But is he really true? How legitimate are his ...
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1answer
172 views

Is mass an inherent property?

Suppose I have an electronic weighing machine placed in a uniform gravitational field. Now I put a mass above it and register the reading. Now I give the system (mass + machine) an impulse so that it ...
3
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2answers
190 views

The Equivalence principle of General Relativity and the Doppler Effect

I am studying General Relativity and am trying to understand the Equivalence Principle more thoroughly. Basically, it is said that if you are in a uniformly accelerated frame of reference in free ...
3
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1answer
202 views

Riemann tensor notation and Christoffel symbol notation

In paper by Barnich and Brandt Covariant theory of asymptotic symmetries, conservation laws and central charges they defined the Riemann tensor like this: $$R_{\rho\mu\nu}^{\quad \ \ ...
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2answers
211 views

Vanishing of the Ricci tensor in higher spacetime dimensions

I understand how, if the Riemann tensor is 0 in all its components, since we construct the Ricci tensor by contracting the Riemann, Ricci tensor would be 0 in all components as well. I've read that ...
0
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1answer
88 views

Does time pass fastest in isolated, resting space?

While it is fairly established that both fast movement and the presence of gravity make time pass slower as compared to a system at rest / free of gravity, does that mean that there is no way for time ...
3
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1answer
158 views

What happens when you apply the path integral to the Einstein-Hilbert action?

The Einstein Field Equations emerge when applying the principle of least action to the Einstein-Hilbert action, and from what I understand the path integral formulation generalizes the principle of ...
2
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1answer
157 views

Is matter a continuous part of the field of space-time? [duplicate]

I recently found this quote by Einstein (in On the Generalized Theory of Gravitation, 1950), and it seems to me like he is saying that matter is a part of the field of space-time, and is nothing more ...