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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77 views

Are all spacetimes locally conformally flat?

No, is the answer. However, I am confused. Let $M$ be a (2+1) Lorentzian manifold (for simplicity) . Then the line element is given by : $ds^{2}=g_{\mu\nu}dx^\mu dx^\nu=−N^2 dt^2 + γ^{ij} (dx^i + ...
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0answers
23 views

Radiation collapse to black hole

I want to find the temperature at which radiation in AdS will collapse to form a black hole. I have even found a reference that gives the answer but I cannot understand it: http://srv2.fis.puc.cl/~...
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0answers
47 views

If black hole is equivalent to a planet of same mass for a distant observer, then why does 'excess radius formula' require uniform mass density?

I understand that the spacetime curvature of a non-rotating, uncharged black hole is identical to that of a planet with same mass/energy for an observer at a distance farther than the radius of the ...
0
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0answers
49 views

How come the cosmological constant supports the idea of dark energy existing? [duplicate]

According to an article I've read recently, the cosmological constant was used to support the theory of dark energy. But the cosmological constant already defines an inclination in the essence of ...
2
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0answers
64 views

What is really going on in the ergosphere of a Kerr black hole?

Considering the Kerr metric with $GM>a$, we can compute 2 event horizons: $r_\pm=GM\pm \sqrt{G^2M^2-a^2}$ These event horizons are null surfaces, and trajectories are timelike between $r_+$ and $...
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1answer
118 views

Black Hole Heat Capacity

Why is the specific heat capacity of a black hole given by $C=\frac{\partial M}{\partial T}$? Heat capacity should be ratio of heat change to temperature change so, denoting heat by $Q$, we have $C=\...
3
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1answer
67 views

Tensor indices and row and column labels of corresponding representation matrices

When reading undergraduate GR literature, I often see that the authors represent tensors ${\eta^\alpha}_{\beta}$, ${\eta^\beta}_{\alpha}$, $\eta_{\alpha \beta}$, $\eta^{\alpha \beta}$ as matrices. ...
2
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1answer
63 views

Is $E = p^0$ in non-inertial frames?

In special relativity the energy of a particle is the 0-component of the 4-momentum. However, is this still true in non-inertial frames, and in particular in non-freely-falling frames in general ...
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0answers
54 views

Is metric $g$ a representation of Lorentz group? What decides it's transformation properties?

I am confused what representation of Lorentz group does a metric transform under? How does it's transformation properties are decided?
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1answer
71 views

Transformation matrices for basis and coordinate transformation in non-orthonormal coordinates

The transformation matrices for covariant and contravariant vectors are different but in orthonormal coordinate system numerical values in matrices turn out to be same although in mathematical proof ...
3
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2answers
192 views

Gravitational waves, tides and the end of universe

Is tides proof of gravitational waves with low frequency? According to Wikipedia, In physics, gravitational waves are ripples in the curvature of space-time which propagate as waves, travelling ...
2
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1answer
81 views

Quasar redshift

The quasar 3C 273 has a redshift z=0.158. A question in a textbook: could this be a gravitational redshift instead of cosmological (=resulting from the expansion of space)? My answer: no. Firstly, ...
2
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0answers
32 views

Momentum and Kaluza-Klein charge

In normal Kaluza Klein reduction over a $S^1$, the momentum round the circle contributes to the electric charge in the lower dimensional theory. I am curious as to whether, under certain ...
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0answers
40 views

What is the physical meaning of the Killing vectors associated to this metric?

I was trying to solve a problem in GR with the following metric: $$ds^2 = -du dv + dx^2 + dy^2 + F(u,x,y) du^2 $$ The coefficients of the metric don't depend on $v$, so $\partial_v$ defines a ...
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2answers
79 views

Kaluza Klein charge

If I take a $(d+1)$ dimensional Einstein Hilbert Lagrangian $L_{d+1}=\sqrt{-\hat{g}} \hat{R}$ and perform a standard Kaluza Klein dimensional reduction by periodically identifying one direction, let's ...
12
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2answers
416 views

Do any quantum gravity theories deal with closed timelike curves?

As far as I'm aware, there are no quantum gravity theories that deal directly with closed timelike curves. Some of them (like canonical quantum gravity, causal dynamical triangulation and loop quantum ...
0
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2answers
91 views

Expansion of the Universe [duplicate]

At what speed is our solar system expanding, and if it is, why don't the positions of the sun and planets change, or grow farther apart? Why is the Big Dipper still where it is?
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1answer
77 views

Why does general relativity need space to be continuous? [duplicate]

http://www.askamathematician.com/2009/12/q-howwhy-are-quantum-mechanics-and-relativity-incompatible/ So I was reading this article because I'm new to this stuff and don't quite understand the ways in ...
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1answer
78 views

How can I calculate the period of a photon in a gravitational field?

I'm taking a course in GR and I want to determine for which radius a photon can move in a circular orbit in the gravitational field produced by a massive spherical body (Schwarzild's metric). What I ...
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1answer
71 views

why does quantumn theory not reconcile itself with general relativity [duplicate]

Why has there not been a resolution in the gravitational effect between the two? It seems that quantum theory and Einstein disagree.
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2answers
132 views

What does diagonalization mean here?

In a gravity theory in spacetime, the metric has signature $− + +· · ·+$. Concretely this means that the metric tensor $g_{μν}$ may be diagonalized by an orthogonal transformation, i.e. $$(O^{-1})_{μ}^...
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0answers
29 views

What does black hole temperature mean? [duplicate]

From the title, the question is a bit open ended. Let me make it a bit simpler. 1. What region of the black hole has temperature? Is it the surface space? the region outside? . . . etc , any precise ...
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2answers
152 views

Gravitational Time Dilation vs Acceleration Time Dilation

I might be a little dense to this subject, but I would like to ask a question relating to this one ( Is gravitational time dilation different from other forms of time dilation? ) but asking if this ...
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0answers
178 views

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 ...
9
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1answer
380 views

Time Dilation inside a hollow shell

Assuming I have a hollow shell with total mass $M$ and radius $r$. On the surface, the gravitational time dilation would be $$\tau=t \cdot \sqrt{1-\frac{v_{esc}^2}{c^2}}$$ where $$v_{esc} = \sqrt{\...
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4answers
380 views

What would be the view like from inside a black hole looking towards the event horizon?

Ignoring the fact that we would be torn apart by gravitational gradient and assuming we get some time to make some observations before hitting singularity, what would we see looking towards the event ...
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0answers
45 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
44 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, ...
0
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1answer
197 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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2answers
92 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$$\vec{e_{r}}=\frac{\partial x}{\partial r}\vec{e_{x}}+\frac{\partial y}{\partial r}\vec{e_{y}.}$$ ...
3
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0answers
46 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 ...
0
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1answer
45 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 $\alpha^{-2}=-g(\nabla f, \nabla f)$...
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0answers
160 views

If gravity is due to curvature, how does gravity work in situations with no curvature?

The strength of the gravitational field falls off as the inverse square of the distance from a spherical source. It only falls off as the inverse of the distance from an extended cylindrical or line ...
0
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1answer
132 views

Black Hole Matter to Subatomic Exchange

When matter enters a black hole with a singularity the particles smaller than photons released come from within the black hole or do subatomic particles shed from matter just before matter passes the ...
3
votes
2answers
169 views

Redshift due to a static gravitational field and the conservation of energy [duplicate]

I am standing on the surface of some planet. Gravity is described via General Relativity with some static metric (e.g. the Schwarzschild metric, so static means no time dependence, but the metric may ...
1
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1answer
51 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 ...
3
votes
1answer
345 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 ...
0
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0answers
32 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 ...
3
votes
1answer
112 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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0answers
27 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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3answers
270 views

How are gravitational waves exactly produced?

I was thinking about gravitational waves, and I found out that I may have a doubt about their production. Assuming the whole calculations find a wave-like solution to be understood, I was wondering ...
0
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2answers
105 views

A manifold question: Why smooth functions and what is a Jacobian?

My question is what does a Jacobian have to do with the change of coordinates (coordinate transformation). Why do we care about this notion to start with? Also, why should it be non-singular?
0
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2answers
102 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 ...
2
votes
2answers
230 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 ...
4
votes
1answer
111 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 ...
2
votes
1answer
117 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 ...
3
votes
1answer
167 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 $\{\partial_\rho\}_{\...
0
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1answer
37 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
94 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. ...
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0answers
58 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 ...