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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1answer
375 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} = ...
11
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4answers
371 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 ...
0
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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
42 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
159 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 ...
1
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2answers
85 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
42 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
39 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 ...
1
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0answers
149 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
131 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
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2answers
152 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
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1answer
256 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
31 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
102 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 ...
1
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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?
1
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3answers
257 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
102 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
93 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
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2answers
202 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
votes
1answer
109 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
115 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
165 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 ...
0
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1answer
35 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
1
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1answer
91 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. ...
1
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0answers
57 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 ...
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0answers
35 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 ...
1
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1answer
116 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, ...
0
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0answers
34 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 ...
0
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2answers
133 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 ...
4
votes
2answers
102 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?
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0answers
39 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 ...
9
votes
2answers
235 views

Symmetry of the Polyakov action?

Let us look at the Polyakov action for a string moving in a spacetime with metric $g_{\mu \nu}(X)$:$$S_P = -{1\over{4\pi \alpha'}} \int d^2 \sigma \sqrt{-\gamma} \gamma^{ab} \partial_a X^\mu ...
1
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1answer
41 views

Equation of state in General Relativity versus microscopic description of the fluid

I can't find the answer to the following question. Consider matter fields in General Relativity, assume it to be a perfect fluid. Then its equation of state is, by definition: $$ w=\frac{p}{\rho} = ...
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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 ...
0
votes
1answer
95 views

Bigger Galaxies = Faster Clocks [closed]

There are in all about 100 known galaxies with blueshifts out of the billions of galaxies in the observable universe. We have Blue-shifted galaxies are in our own local group, and are all bound to ...
1
vote
3answers
283 views

Time Dilation Equals Red Shift looking in or blue shift looking out

We can see the center of our galaxy. With more density near the center of our galaxy is red shifting observed from our perspective? From the center of the galaxy looking at us would a blue shift be ...
1
vote
1answer
139 views

How long ago, and how far away, could “A long time ago in a galaxy far, far away” have been? [closed]

Assume an event happened "A long time ago in a galaxy far, far away", and assume this event includes intelligent carbon-based life forms. What are bounds$^{a}$ on the time and distance (from us) of ...
1
vote
1answer
45 views

What is the property which flows as described by the stress energy tensor in GR?

I found the following definitions: The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of ...
3
votes
0answers
50 views

What is the inertial mass of a black hole?

Or the inertial mass of any spherically symmetric object, can I calculated by measuring very accurately the spacetime distortion this object produces in its surroundings? With 'inertial mass' I mean ...
0
votes
1answer
69 views

Acceleration of a static observer in Schwarzschild measured in locally inertial frame [closed]

Consider a static observer at $r=R>2M$ with four velocity given by $$U^\mu=\frac{dx^\mu}{d\tau}=(1-\frac{2M}{R})^{-1/2}\delta^\mu_0$$ in the Schwarzschild metric ...
0
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0answers
45 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 ...
0
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3answers
115 views

How does a mass create the gravitational field of GR? [closed]

As far as I understand, and please correct me if I am wrong, but the basic idea of general relativity is that spacetime is curved by matter. What we call gravity is then not a force as per Newton but ...
0
votes
2answers
211 views

When sitting on a chair is it the chair actually pushing against me?

I was listening to The Infinite Monkey Cage on the BBC and they were talking about general relativity and gravity. They were saying that gravity is not a force as Newtonian laws describe and is at ...
5
votes
1answer
207 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
votes
0answers
100 views

How to understand the relationship between these two geometrical structures?

During my study of quantum information processing, I occasionally meet two different geometrical structures: (a) The geometry of the Hilbert space of quantum state, where the superposition and ...
2
votes
1answer
52 views
1
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2answers
123 views

Why does a light wave fade as it travels through space?

It stands to reason: if it didn't, the entire sky would be covered with stars shining blindingly day and night. But what causes a light wave (or an electromagnetic wave) to fade if there are no ...
0
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0answers
54 views

Could we have blue/violet shifting?

As the universe expands, it stretches light into longer wavelengths, resulting in what we know as red shifting. But some say that there is a chance in which the universe will stop expanding and then ...
0
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2answers
119 views

Is causality a total order?

I've read that it is physically not possible to violate causality defined as a total order on the spacetime graph. So I was wondering if at least causality can be broked down to a partial order and if ...