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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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
6k 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
254 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
218 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
319 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
374 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 ...
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1answer
100 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
190 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
242 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
101 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
137 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
71 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
230 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
212 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
286 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
155 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
373 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
254 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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2answers
527 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
238 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 = ...
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4answers
1k 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
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3answers
804 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
346 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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3answers
1k 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
110 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
129 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
233 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
373 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 ...
4
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4answers
1k views

Why acceleration is not relative in General Relativity?

I was thinking of it, If I say: "I'm moving at a velocity $v_1$ relative to a reference frame $M$ then the acceleration will be the derivative of $v_1$ relative to the reference frame $M$." In other ...
6
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2answers
624 views

Parallel Transport of a 4-vector

Why does the parallel transported $4$-vector change from $X^a(x)$ to $X^a(x) + \bar{\delta}X^a(x)$ ? This is also discussed in D'Inverno's relativity book [page - 72]; but the reason is not clear.
3
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1answer
125 views

On Einstein's equivalence principles

There are two foundative Equivalence Principles in General relativity: Weak Equivalence Principle (WEP): the dynamics of a test particle in a gravitational field is independent of its mass and ...
2
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2answers
391 views

Weight of a tensor density

Is there any freedom in choosing the weight of a tensor density? I have seen in some papers that they introduce a tensor density made from metric with a special weight. There is a tensor density with ...
2
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0answers
53 views

Is it possible that a matter field has a dependent on non-radial space-like coordinate in a spacetime with spherical symmetry?

After the work from Breitenlohner and Freedman, we know matter fields in asymptotically AdS spacetime can be stable out of the black hole under some special conditions. My question: In such a ...
8
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1answer
338 views

Is a QFT in a classical curved spacetime background a self-consistent theory?

EDIT: Better rewording by Chris White: Is it possible to have a theory that treats both GR and QFT (e.g. QFT on a curved spacetime dynamically influenced by the standard QFT fields)? Is such a theory ...
2
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1answer
319 views

Showing that the variation of an affine connection is a tensor

How can i show that $\delta\Gamma_{\mu\nu}^{\rho}$ transforms like a tensor? Metric compatibility is not assumed here. That means 1) First i need to compute $\delta\Gamma$ first. To do that i need ...
16
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2answers
400 views

In relativity, can/should every measurement be reduced to measuring a scalar?

Different authors seem to attach different levels of importance to keeping track of the exact tensor valences of various physical quantities. In the strict-Catholic-school-nun camp, we have Burke ...
3
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1answer
1k views

'Easy way' of finding out the Killing vector fields?

Is there a way for calculating the Killing vector fields of a given metric in a quick way? Sure I can guess looking at the metric at the symmetries, and then guess some of them, but, for instance, in ...
10
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1answer
439 views

Can masses move in 2+1 gravity?

I would like to understand basic concepts of the general relativity in 2+1 spacetime. As far as I know, GR predicts that such a spacetime is flat everywhere except for the point masses which create ...
5
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1answer
466 views

Naive quantum gravity

My question involves an analogy I have to point out. Consider the Lagrangian density for the a complex scalar field: \begin{equation} ...
2
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2answers
137 views

Distinguish between Past and Future

When writing the metric in Minkowski space, how can we distinguish between the past and the future? I understand the answer after drawing the light cone but I want to know how we get that by just ...
3
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1answer
2k views

Riemann tensor in 2d and 3d

Ok so I seem to be missing something here. I know that the number of independent coefficients of the Riemann tensor is $\frac{1}{12} n^2 (n^2-1)$, which means in 2d it's 1 (i.e. Riemann tensor given ...
8
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2answers
666 views

Surface gravity of Kerr black hole

I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand. Firstly, the metric is given by ...
3
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0answers
188 views

Schwarzschild metric in a different coordinate system

In PADMANABHAN, Gravitation (Foundations and Frontiers), Cambridge, p $304$, exercice $7.6$, an example of the Schwarzschild metric in a different coordinate system is given : $$\mbox{d}s^2= ...
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0answers
52 views

Geodesic in general relativity aproaching ellipse

In the gravity well-like 2d surfaces that are used in documentaries to illustrate the fact Earth orbits the Sun, I don't seem to find any kind of geodesic that will at least resemble an ellipse... ...
5
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1answer
187 views

Quantization surface in QFT

What does the Quantization Surface mean here? Reference: H. Latal W. Schweiger (Eds.) - Methods of Quantization
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1answer
75 views

Getting diffeomorphisms from boundary conditions in $AdS_3$

As usual I'm asking a question about boundary conditions for AdS${}_3$, based on the thesis by Porfyriadis. He is solving equations $\mathcal{L}_\xi g_{\mu\nu}$ for AdS${}_3$ metric, with a given ...
3
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2answers
1k views

Equation of everything

Is this equation in the image true? Can you give some topics that I can cover the equation.
5
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2answers
412 views

Asymmetric Schwarzschild solution - unequal mass on each side

Look at any Kruskal–Szekeres coordinate plot of the Schwarzschild solution. It shows the same mass everywhere. Yet the two sides cannot talk to each other, in that no information, particles, etc can ...
3
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2answers
344 views

Is spacetime all that exists?

Someone claiming to have studied physics is telling me that spacetime is all that exists and that this fact is the basis of modern physics. When I said matter/energy also exists in its various forms, ...
6
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1answer
187 views

Equilibrium for a rope hanging in a Schwarzschild spacetime

Update: Trimok and MBN helped me solve most of my confusion. However, there is still an extra term $-(2/r)T$ in the final result. Brown doesn't write this term, and it seems physically wrong. Update ...