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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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
116 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
65 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
227 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
1k 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
600 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 ...
3
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1answer
120 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 ...
12
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1answer
727 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
202 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 ...
6
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1answer
300 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
352 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
100 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
2k 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 ...
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2answers
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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 ...
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2answers
670 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 ...
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1answer
223 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
36 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
111 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 ...
20
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4answers
864 views

How Come gravity doesn't affect itself?

If gravity is this "unexplainable force" that pulls everything to the center of a planet or stellar remnant you stand upon, why doesn't gravity pull itself? If gravity affects anything with energy, ...
6
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1answer
717 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
582 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
242 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
247 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
9k 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
339 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 ...
4
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2answers
261 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
446 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
647 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
113 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 ...
6
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3answers
343 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
410 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 ...
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1answer
121 views

Diagonal stress energy tensor components

If I got a diagonal stress energy tensor $T_{\alpha \alpha} = x_{\alpha}$ for some coefficients $x_{\alpha}$, could anyone tell me how can I extract the four components of the stress energy tensor. ...
3
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0answers
155 views

Is the equivalence principle in General Relativity an approximation?

I read in web that Einstein used the principle of equivalence to explain General Relativity but we know the gravitation is approximately equal in all of rested frame in gravitional field. In ...
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0answers
75 views

Present experimental status of Moffat's Modified theory of Gravity

Modified theories of Gravity have been discussed before in this 2-year old question, Are modified theories of gravity credible? I was going through Moffat's modified gravity, given in ...
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1answer
395 views

Transformation rule of a partial derivative

We know the following transformation rule: $$ \partial'_b = \frac{\partial}{\partial x'^b} = \frac{\partial x^c}{\partial x'^b} \, \frac{\partial}{\partial x^c} = \frac{\partial x^c}{\partial x'^b} ...
4
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1answer
266 views

Why is there a gravitational attraction between two objects at rest with respect to each other?

From my understanding of relativity, gravity is not a force, but a result of the curvature of spacetime. If Object1 moves past Object2, even though it's moving in a straight line, its direction may ...
6
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1answer
482 views

Schwarzschild solution in arbitrary dimensions

Is there any generalized Schwarzschild solution for an arbitrary number of dimensions? Is it necessary to calculate each individually, or is there a relationship between them?
7
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1answer
213 views

What's the relation between the Euler $\psi$ function, the digamma function, and the hypergeometric function?

Can somebody help me out with the intermediate details of eqn. (2.5) in this paper? Generalized gravitational entropy. Aitor Lewkowycz and Juan Maldacena. arXiv:1304.4926. Is the Euler $\psi$ ...
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2answers
527 views

Can a scalar field model gravity? How accurate would be the results? Are there any difficulties with such a model?

Newtonian gravity can be described by the equation: $$ \nabla^2 \phi = 4 \pi \rho G $$ where $\rho$ is the mass density, $\phi$ is the gravitational potential, and G is the universal gravitational ...
2
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1answer
324 views

Does the concept of a wormhole violate the law of mass-energy conservation?

If my understanding of wormholes is correct, anything that moves into a wormhole can be transported from one region of space-time to another. Consider a situation where an object of mass $m$ in space ...
2
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3answers
759 views

Notation for anti-symmetric part of a tensor

I know that $A_{[a} B_{b]} = \frac{1}{2!}(A_{a}B_{b} - A_{b}B_{a})$ But how can write $E_{[a} F_{bc]}$ like the above? Can you provide a reference where this notational matter is discussed?
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3answers
264 views

Coordinate transformations of the metric tensor

Let's have metric (it describes the space-time of uniformly accelerating observer in Minkowski space-time) $$ ds^2 = v^2du^2 - dv^2. \qquad (.0) $$ I need to find expressions for $u = f(x, t), v = ...
16
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4answers
2k views

Can matter really fall through an event horizon?

This question is closely related to Event horizons without singularities from about a year ago (May 2012), which John Rennie answered nicely and persuasively. My variant of the question is this: ...
8
votes
3answers
981 views

Covariant and contravariant vectors

Reading Weinberg's Gravitation and Cosmology, I came across the sentence (p.115, above equation (4.11.8)) The partial derivative operator $\partial/\partial x^\mu$ is a covariant vector, or in ...
2
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1answer
429 views

Check it the Killing vectors satisfy Killing equation or not

I am going through Kerr/CFT correspondence paper again, and I am at the section where authors specify Killing vectors for near horizon extreme Kerr metric (shortly NHEK). The metric is ...
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2answers
2k views

Why gravity is an attractive force? [duplicate]

Why gravity is an attractive force? One may say that it is because of space time curvature but General Relativity is built on this law: $\displaystyle G \frac{m_1 \times m_2}{r^2}$ (To be more ...
2
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2answers
117 views

Whose reference frame to use for $d \theta$ near a black hole?

Using the Schwarzchild metric for a body circularly orbiting a nonspinning black hole (i.e. $dr=0$), the relation between $d\tau$, the time between two light pulses sent out infinitesimally close ...
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1answer
153 views

General Relativity and Time Dilation [duplicate]

Is time affected by the gravitational force? If so, what might be the effect on time at the centre or near centre of earth ?
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2answers
368 views

Raising indices in Killing equation or not?

I'm having issues with computation of Killing equation. I'm using Mathematica to check if the given vectors are Killing vectors or not, and by hand for simple vector like $\xi=\partial_t$ I get the ...
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3answers
425 views

Is it true to say *Space time curvature* $\Leftrightarrow$ *Matter*

Is it true to say Space time curvature and Matter are just the same thing, part of the same coin and that therefore Space time curvature $\Leftrightarrow$ Matter? In other words is Space time ...