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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When is the event horizon a Killing horizon?

I know the definition of both (event horizon is closure of causal past of future null infinity whilst Killing horizon is a null surface where some Killing vector becomes null e.g. the surface where it ...
12
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7answers
654 views

Can a ultracentrifuge be used to test general relativity?

With today's ultracentrifuge technology, they can spin so fast that the sample can be subjected to accelerations of up to 2 millions Gs. That is equivalent to two solar masses. Has someone tried to ...
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1answer
83 views

Intuitive meaning of Globally Hyperbolic

I am been studying differential geometry and spacetime and I keep coming across the term globally hyperbolic. I am having a hard time coming up with an intuitive understanding of this idea. What is an ...
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0answers
31 views

General relativity degrees of freedom — simplified version?

I'm afraid my question may be too general, but I would like to ask how I could find out the degrees of freedom in a given tensor. I have had this question since I started studying GR. At first, I ...
2
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0answers
36 views

Does entropy flatten spacetime?

Forgive me if this is a non-question, but I could not find anything regarding this. I only know parts of GR, and I am not familiar with the math. Since energy and matter density curve spacetime, ...
3
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1answer
56 views

Are closed timelike curves generic feature of ANEC-violating stress-energy tensor?

Kip Thorne has shown that in order to create closed timelike curves (CTCs), one needs stress-energy tensor $T^{\mu\nu}$ that violates averaged null energy condition (ANEC). Will $T^{\mu\nu}$ with ...
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3answers
1k views

Why space expansion affects matter?

If space itself is expanding, then why would it have any effect on matter (separates distant galaxies)? Space is "nothing", and if "nothing" becomes bigger "nothing" it's still a "nothing" that ...
3
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1answer
99 views

Einstein tensor of a gravitational source

In section 4.4 of gravitational radiation chapter in Wald's general relativity, eq.4.4.49 shows the far-field generated by a variable mass quadrupole: $$ \gamma_{\mu \nu}(t,r)=\frac{2}{3R} \frac{d^2 ...
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2answers
239 views

How warped spacetime bends trajectories of light and moving objects?

I fail to see why the light follows something like the blue line and not the green line on the attached image. Figure 1 - light bends around warped spacetime Afaik. something similar happens ...
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1answer
77 views

Apparent Horizon vs. Event Horizon

I understand that an apparent horizon is the boundary of trapped codimension-2 surfaces in the spacetime (surfaces from which both ingoing and outgoing light rays must be converging). Meanwhile, an ...
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2answers
66 views

Two ways of writing coordinate basis vectors confusion

In Schutz's A First Course in General Relativity (p122) he derives the polar coordinate basis vector$$\vec{e_{r}}=\frac{\partial x}{\partial r}\vec{e_{x}}+\frac{\partial y}{\partial r}\vec{e_{y}.}$$ ...
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34 views

“Simple” Variation of the gravity action with boundary

I'm concerned with the derivation of the quasi-local stress tensor (getting from eqn 2.4 to eqn 2.6 in this paper: http://arxiv.org/abs/hep-th/0508218). As is the case with all the references I have ...
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1answer
35 views

Calculate lapse function from the metric

I have a technical question about the lapse function: Assume I have some given (Lorentzian) metric $g$. I have seen the following definition of the lapse function $\alpha^{-2}=-g(\nabla f, \nabla ...
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0answers
27 views

Easy unit conversion in Kerr metric

I would like to use Kerr metric in Boyer-Lindquist coordinates in geometrized units with mass of the black hole normalized to $M=1$. I am embarrassed to admit, but I can't seem to figure out how to ...
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3answers
125 views

When a neutron star accumulates enough mass, does a black hole start at its center?

With less dense bodies, such as the earth and the sun, the center has less gravity/density (since there's an equal amount of mass surrounding the center, pulling out on it from all directions). Does ...
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1answer
93 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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6answers
255 views

In GR, why should the spacetime manifold be differentiable?

In general relativity (GR), spacetime is viewed as a differentiable manifold of dimension $D$ with a metric of Lorentzian signature $(-,+,+,...,+)$. My question is why differentiable?
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1answer
36 views

Help with the Ricci tensor and Chistoffel Symbols [closed]

I really am confused with certain notations of the Ricci tensor and the Christoffel symbols. I'm looking to evaluate $R_{00}$ from my lecture notes, but I'm a little stuck at one point. The Ricci ...
2
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1answer
86 views

How should Christoffel symbols be written (in LaTeX)? [closed]

I'm writing a summary of a lecture on relativity, and we've recently introduced the Christoffel symbols. It seems that the upstairs indices are the "leftmost" and the downstairs indices are somewhat ...
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1answer
170 views

What is gravitational energy in general relativity?

In GR the curvature of spacetime "is gravity". This curvature is expressed via the Riemann tensor (or the Ricci tensor + Ricci scalar). The curvature is connected via the Einstein Field Equations with ...
2
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1answer
99 views

Derivation of Schwarzschild metric using the full machinery of differential geometry [closed]

How would one derive the Schwarzschild metric using the full machinery of differential geometry, using the component approach as little as possible? Something along these lines: Begin with a manifold ...
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0answers
36 views

Simple tetrad exercises

I am reading Andrew Hamilton's really nice notes on Tetrad formalism of general relativity, and I am having trouble finding assignments/exercises on tetrad formalism. Would anyone know a good resource ...
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0answers
49 views

Gravitational wave as a consequence of gravity being a field

I was reading an online article about gravitational wave detection and there is a sentence which says: The existence of gravitational wave is simply a consequence of the fact that gravity is a ...
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1answer
747 views

Do intergalactic magnetic fields imply an Open Universe?

According to a paper on the arXiv (now published in Phys Rev D), they do. How credible is this result? The abstract says: The detection of magnetic fields at high redshifts, and in empty ...
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0answers
26 views

If gravitons are particles, how do they escape BH gravity if nothing can? [duplicate]

If gravitons are particles, how do they escape BH gravity if nothing can? So are the gravitons really particles or is there really just/only curvature of space-time?
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2answers
73 views

What does coordinate invariance mean?

I would like to really understand what the mathematical as well as Physical meaning of coordinate invariance is. I have pretended to know what this means, but upon thinking a little harder today, I am ...
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1answer
94 views

Black hole merger orbital speed

If a ship is close to a black hole and we see it getting slower to the point if could see them not for red shift would almost stop moving. Then how fast is the little black hole moving in this video? ...
3
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1answer
129 views

Repeated index in covariant derivative using abstract index notation

The same index showing up twice in the charge conservation law $\nabla_a j^a = 0$, as stated using abstract index notation, highly confuses me. If we chose a coordinate basis ...
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2answers
80 views

What is the metric tensor for?

I am wondering how to use the metric tensor, in practice? I read the book and done the exercises in A student's guide to vectors and tensors by Dan Fleisch. The concept of a tensor and their ...
3
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2answers
200 views

The ADM Energy of Gravitational Waves?

I have been looking for books about this question for several days. However, almost all books use Landau–Lifshitz pseudotensor to calculate the energy of Gravitational Waves.And they said the result ...
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1answer
28 views

Inverse gauge transformation in general relativity [closed]

Can someone explain to me how (8.21) follows from (8.20). The Picture comes from A first course in general relativity (Schutz). Thanks and regards, Jens Wagemaker
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1answer
77 views

Why do we introduce the idea of manifold in GR books

After reading Timaeus answer here: http://math.stackexchange.com/questions/1302672/compound-map-in-manifolds, I got an idea that spacetime we usually talk about in GR can be described as a manifold. ...
3
votes
3answers
502 views

Clarifying what metric counts as flat space

In (2D) Cartesian coordinates, the Euclidean metric... $$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$ ...is flat space. If the diagonal elements are exchanged for other real numbers ...
7
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3answers
602 views

Using a black hole as a mirror

http://www.youtube.com/watch?v=ENd8Sz0AFOk The YouTube video is a good example how the gravity of this merging binary black holes bend light around themselves.
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1answer
48 views

Is there inflationary solution in $R^2$ theory in Jordan frame?

In the Starobinsky $R^2$ inflation model, one usually uses a conformal transformation from Jordan frame to Einstein frame in which the action can be written just like Einstein action + scalar field ...
2
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2answers
167 views

Timelike Boundary

I was reading in a paper (see 1st paragraph of introduction section in http://arxiv.org/pdf/1510.00709.pdf) that in AdS space, waves can reach the boundary in finite time and, since said boundary is ...
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0answers
21 views

Comoving and physical momentum in a Friedmann universe

It is most probably a very basic question, but I'm a bit stuck with it. Let us consider a spatially flat Friedmann universe with the usual metric ...
2
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1answer
120 views

The Einstein-Cartan equation as the “living heart of gravity”?

I recently read in A Journey into Gravity by Wheeler that "The Einstein-Cartan equation gives us the most vivid image that mankind has ever won of the living heart of gravity" (P.118) ...
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2answers
1k views

Is time going backwards beyond the event horizon of a black hole?

For an outside observer the time seems to stop at the event horizon. My intuition suggests, that if it stops there, then it must go backwards inside. Is this the case? This question is a followup ...
1
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1answer
102 views

Why pseudo-Riemannian metric cannot define a topology?

It is not clear for me why a positive definite metric is necessary to define a topology as noted in some textbooks like the one by Carroll. Does this imply that in cosmology, say through FLRW metric, ...
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0answers
32 views

Why is spacetime curved by mass but not charge [duplicate]

According to general relativity theory, the deformation of spacetime is proportional to energy tensor $$T_{\mu\nu}.$$ $$ R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi G T_{\mu\nu}. $$ Does it mean that ...
3
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1answer
806 views

$N$-body simulation in General Relativity

How would one perform an $N$-body simulation in General Relativity (GR) for something like galaxy formation or galactic dynamics? Suppose one wants to simulate the rotation curve $v(r)$ for galaxies ...
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2answers
93 views

Redshift of distant galaxies: why not a doppler effect?

How can I explain to my 17 year old pupils that the observed redshift of distant galaxies cannot be interpreted as a doppler effect and inescapably leads to the conclusion that space itself is ...
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0answers
43 views

Direction of Gravity [duplicate]

I ran into a pde that has a parameter in it that can be either $+1$ or $-1$. They say the $+1$ case corresponds to gravity pointing upwards, whereas the $-1$ case applies to gravity pointing ...
15
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4answers
651 views

The problem of self-force on point charges

Allow me to preface this by stating that I am a high school student interested in physics and self-studying using a variety of resources, both on- and off-line, primarily GSU's HyperPhysics website, ...
3
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2answers
282 views

Communication back in time?

On the wikipedia page for time travel, it mentions that Robert Forward said (theoretically, unknown since we don't have a working theory of quantum gravity) that if a heavy nucleus was subjected to an ...
3
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2answers
74 views

Does metric signature affect the stress energy tensor?

If one were to derive the stress-energy tensor for a metric with $(+,-,-,-)$ signature would it be different from the stress-energy tensor derived from the same metric but with $(-,+,+,+)$ signature?
2
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2answers
94 views

Gravitational lensing and perspective

When looking at a black hole the ability to see ourselves is compromised by the small window for the light trajectory to come back to us. The light from the Earth that is bent by (almost) 180° and ...
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1answer
78 views

Time independent Kerr metric

The Kerr metric expressed in terms of polar coordinates $r,\theta,\phi$, such that $x = r\sin(\theta)\cos(\phi)$, $y = r\sin(\theta)\sin(\phi)$, $z = r\cos(\theta)$. Then the Kerr metric is given as ...
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0answers
36 views

Is it possible to define a symmetry group for the Einstein metric?

I was just wondering if there exists a group of transformations that act on the metric such that the EFE are invariant. At first I thought it would be the group of 2nd roots of unity. That is, the set ...