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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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
262 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 ...
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104 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?
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97 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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2answers
216 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 ...
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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 ...
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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 ...
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1answer
166 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\}_{\...
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1answer
36 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
92 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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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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38 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 $$ds^2=dt^2-a^2(t)\left(dr^2+r^2d\vartheta^2+r^2\sin^...
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1answer
117 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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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 ...
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2answers
145 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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2answers
106 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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40 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 ...
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238 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 \...
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1answer
42 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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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 downwards....
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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 ...
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3answers
292 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 ...
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1answer
142 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 ...
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1answer
46 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 ...
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58 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 ...
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1answer
76 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 $$ds^2=-(1-\frac{2M}{r})dt^2+(1-\...
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47 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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3answers
121 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 ...
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2answers
243 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 ...
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210 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 ...
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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 ...
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1answer
52 views
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127 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 ...
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55 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 ...
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2answers
122 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 ...
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15 views

Angular Optical Resolution [duplicate]

Can a series of optical telescopes from orbit (like the radio Event Horizon Telescope) see an object with higher resolution not possible with one telescope?
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2answers
128 views

With gravitational lensing could we see our selves from a right angle?

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
116 views

Simple metric of stellar collapse

Is there a simple metric (Lorentzian manifold) known which exhibits the formation of a black hole while not having any white hole counterpart and which moreover satisfies the strong and dominant ...
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1answer
75 views

Proving that Killing form contractions with geodesics are constants of motion

I want to prove the fundamental theorem of Killing forms, namely that $$\frac{d}{d \lambda} \Big( \frac{d P^{\mu}}{d \lambda} \xi_{\mu}(P(\lambda)) \Big) = 0 $$ If $P(\lambda)$ is a Geodesic curve,...
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1answer
66 views

Einstein tensor as a conserved current?

As is well-known, the ``traditional" conserved quantities (energy, momentum...) are Noether currents whose conservation depends on the existence of various Killing fields in Minkowski space. In ...
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2answers
121 views

Why can't gravitational force have repulsive counter part?

The valleys in the space-time curvature signifies the existence of an attractive body which causes the curvature. So why can't we say that the hills in the fabric of space-time is a source of ...
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20 views

relativity, light, transformations [duplicate]

is the light itself a reference frame in special relativity? Can we write the special relativity transformations between a photon and other reference frames? If we can't then what other transformation ...
4
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4answers
251 views

Can there be acceleration without velocity?

If I was in a spaceship continually accelerating at $9.81m/s^2 =1g$ in a straight line, I would reach near light speed within a year. On Earth, we are in a gravitational field of $1g$, which ...
3
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1answer
89 views

The Riemannian Penrose Inequality in higher dimensions

I am reading the proof of the Riemannian Penrose Inequality by Huisken and Ilmamen in The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality and I was wondering why they restrict their ...
5
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3answers
406 views

Zero $g$ in a black hole?

At the very centre of the Earth, masses cancel each other out, creating an effective zero-$g$ environment. Would the same happen in a black hole?
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192 views

What is the physical meaning of the Levi-Civita connection?

I'm taking a course in General Relativity and I have studied the fundamental theorem of Riemannian geometry: Let $M$ be a manifold with metric $g$. Then exists an unique torsion-free connection $\...
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1answer
123 views

I do not understand this comparison?

It is frequently discussed that to find solutions having some sort of supersymmetry is easier than solving Einstein’s equations of motion. I do not understand this discussion though. Specifically, ...
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2answers
152 views

Why supergravity is extension of GR?

Why is it that supergravity is an extension to general relativity? In what ways? What I have read until now says the following: GR got itself concerned with gravity after the revolution of special ...
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1answer
48 views

Rocket or elevator?

I realize the gravitational effect in a rocket can be equivalent to the gravity on the surface of Earth. I always hear there is no way to tell the difference between the two but if there were what are ...
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45 views

The spatial Schwarzschild metric

The Schwarzschild spacetime is defined by the following line element \begin{equation*} ds^2 = - \left( 1 - \frac{2m}{r} \right)dt^2 + \frac{1}{1-\frac{2m}{r}}dr^2 + r^2 d\theta^2 + r^2\sin \theta^2 d\...