A theory that describes how matter produces and responds to 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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What's the definition of incompleteness of a coordinate system and a spacetime?

I always see in GR textbooks that some coordinates or some spacetime is incomplete, such as Rindler spacetime and spacetially flat FRW universe with only positive cosmological constant. This ...
3
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0answers
44 views

Does Hawking radiation need an apparent horizon and when does it switch on during stellar collapse?

I've read that Hawking radiation is implicitly linked with the existence of an apparent horizon (1). This seems a slightly less onerous than linking Hawking radiation with a genuine bona fide event ...
2
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2answers
148 views

Does General Relativity correctly explain the ellipsoidal shape of the earth?

Does General Relativity theory correctly explain the ellipsoidal shape of the earth? It seems it does not because the Thirring expression¹ for the force of a spherical shell—of mass $M$, radius $R$, ...
2
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1answer
100 views

Geodesic equation from Euler - Lagrange

There are several ways to derive the geodesic equation. One of which is the variational method which I seemed to understand it because it was written in great details. Then it was mentioned that the ...
3
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2answers
99 views

Could Dust Equation of State have some negative pressure?

Traditionally the cosmological equation of state of cold matter (so-called dust) is simply: $$p = 0.$$ But, in Newtonian terms, each particle is gravitationally attracting every other particle. ...
0
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0answers
60 views

How strong is the force of space expansion?

There are many questions about space expansion, its cause, or its effects. But I have the feeling we never get straight and simple answers. I do not expect answers to be simple in general, but I ...
8
votes
3answers
674 views

Do gravitational fields exist in vacuum region?

I was reading about "vacuum solution" in wiki, http://en.wikipedia.org/wiki/Vacuum_solution_(general_relativity). There are some words I'm confused. 1.In general relativity, a vacuum solution is a ...
2
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1answer
248 views

Black Holes can't exist?

So in this article here, Mersini-Houghton says that Black Holes can't exist. Is there any truth to this? references: http://arxiv.org/abs/arXiv:1406.1525 http://arxiv.org/abs/arXiv:1409.1837
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0answers
37 views

Weak Equivalence Principle and universality of free fall

I know how we can derive geodesic equation from varying the action of a test particle with respect to coordinates and i know the fact that particles follow geodesics means that free fall is universal. ...
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1answer
77 views

Gravity of the accelerated particle in General relativity?

Suppose heavy particle or body ("billiard ball") is accelerated with very thin and very rigid (not absolutely rigid) rod of infinitesimal (not zero) mass ("cue stick") Acceleration is constant in ...
47
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3answers
5k views

Did the Big Bang happen at a point?

TV documentaries invariably show the Big Bang as an exploding ball of fire expanding outwards. Did the Big Bang really explode outwards from a point like this? If not, what did happen?
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1answer
44 views

Are there any difference between gravitational potential of different types of black holes?

There are four possible types of black holes that could exist in the theory of gravitation (called general relativity). Are there any difference between the value of gravitational potential of these ...
1
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1answer
108 views

Is relativistic event horizon half of Newtonian event horizon?

Is Relativistic event horizon half of Newtonian event horizon? relativistic escape velocity formula (from $m\phi=E-E_0$) is $v_e=\sqrt{2\phi-(\frac{\phi}{c})^2}$ and the Newtonian version of the ...
4
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1answer
79 views

Can light produce weak gravitational waves?

I have read online that light can produce a weak gravitational field (for example antiparallel beams should, in principle, attract weakly). This made me wonder if light can produce minute ...
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0answers
38 views

What is Mathematical equation of gravitational waves? [duplicate]

The Cosmic catastrophe is a thought experiment in which the sun were to instantaneously disappear. The question is what would then happen to the Earth? the disappearance of the Sun would create ...
8
votes
1answer
234 views

How does the Hubble parameter change with the age of the universe?

How does the Hubble parameter change with the age of the universe? This question was posted recently, and I had almost finished writing an answer when the question was deleted. Since it's a shame to ...
2
votes
1answer
87 views

Can these two terms cancel out?

In trying to prove that $$\Gamma_{\mu\nu\lambda} = \eta_{ab}J^a_bJ^b_{\nu\lambda}.$$ The author canceled out while expanding the first equation $$J^a_{\mu\lambda}J^b_\nu$$ with ...
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2answers
221 views

Differentiation in general relativity

If we have: $$ \frac{d\phi^a}{d\tau}= \frac{\partial \phi^a}{\partial x^\mu} \frac{dx^\mu}{d\tau} \tag{1}$$ Differentiating it, we get: $$ \frac{\partial \phi^a}{\partial ...
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1answer
43 views

Simplifying Friedmann's Equation

So we have one of Friedmann's equation: $$\rho_c = \frac{3H^2}{8\pi G}$$ Using This website, resources where gathered for specific times in the universe. The resources being the Hubble constant at ...
2
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0answers
45 views

Boundary term in Einstein-Hilbert action

Why is the boundary term in the Einstein-Hilbert action, the Gibbons-Hawking-York term, generally "missing" in General Relativity courses, IMPORTANT from the variational viewpoint, geometrical setting ...
2
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0answers
64 views

How to prove the energy of gravity in general relativity is non-local?

Every textbook in general relativity containing the energy of gravity all says that the energy of gravity is non-local and every energy-momemtum density received is pseudo-tensor, but "having not ...
0
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1answer
45 views

Friedmann equations question

Friedmann equations for critical density is: $$\rho_c = \frac{3H^2}{8\pi G}$$ Is there any other way to write this equation? For example: $$\rho_c = \frac{3}{8\pi GH^2}$$ I saw the above form on ...
1
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1answer
54 views

Riemann Curvature Tensor Symmetries Proof

I am trying to expand $$\varepsilon^{{abcd}} R_{{abcd}}$$ by using four identities of the Riemann curvature tensor: Symmetry $$R_{{abcd}} = R_{{cdab}}$$ Antisymmetry first pair of indicies ...
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0answers
34 views

problem with spin connection term

While working out Kaluza Klein compactification, I am getting the unwanted spin connection term $\omega_{c}^{ac}$ .I have tried to show that this is zero.But I am not quite sure of it. What I tried ...
5
votes
3answers
112 views

Concept of worldline

My family tree (me, my parents, their parents, etc.) is obviously set in time, with of their birth dates denoting a node. Can such a family tree be viewed as an abstract form of a worldline? Why or ...
0
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1answer
62 views

Electromagnetism in flat space

I want to get a deeper understanding of how Electric and Magnetic fields transform under Lorentz transformation. That is how to start from gauge transformation of Electric and Magnetic fields $$E= ...
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2answers
48 views

Recommendation on ADM mass and Bondi mass

I want to learn some advanced topics in GR, such as ADM 4-momentum and Bondi 4-momentum. However nearly no textbooks on GR contain this area, such as Wald, MTW, Hawking, Carroll and Zee's. Can anyone ...
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37 views

Relation involving the Lorentz transformation and the inverse of its transpose

The relation I was referring to in the title is $${\Lambda_a}^b= \eta_{ac} {L^c}_d \eta^{db}$$ where ${\Lambda_a}^b$ is the inverse transpose of $L$, the Lorentz transformation. I was wondering ...
4
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1answer
108 views

Is the zero acceleration path also the shortest path between two points?

In flat, free, Euclidean space, the shortest path and the zero acceleration path are the same path, which is a straight line. However, in general relativity, is the zero acceleration path also the ...
0
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1answer
137 views

How do objects even move due to gravity?

I am an newbie general relativistic learner and I learnt that gravity is bending of space-time and since objects move in straight-lines but since its curved they follow curved movement through space ...
2
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0answers
71 views

What are Killing spinors?

What are Killing spinors? How can they be motivated? Are they directly related to Killing vectors and Killing tensors and is there an overarching motivation for all three objects? Any answer is ...
2
votes
1answer
90 views

How does string theory describe classical gravity theory, and QFT? [closed]

I am learning string theory, as I understand, gravitons exist as modes in string excitations, and also other particles. It gave me this picture: a lot of strings fulling in the spacetime, excitations ...
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0answers
54 views

Equation regarding the Riemann tensor in the Cartan formalism [closed]

I have a problem verifying the following equation (in three dimensions) $$\epsilon_{abc} e^a\wedge R^{bc}=\sqrt{|g|}Rd^3 x$$ where $R$ is the Ricci scalar and $R^{bc}$ is the Ricci curvature ...
3
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0answers
59 views

Ricci curvature of embedded spacetime

If I am not mistaken, there is a theorem which states that every Riemannian manifold can be embedded in the $n$-dimensional Euclidean space for some large-enough $n$. Does it also hold for ...
4
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4answers
161 views

Applications of the Linearized Einstein Field Equations (EFE)

Look up linearized Einstein field equations anywhere and the first thing you'll see will be a discussion of gravitational waves. Using the linearized EFE's is pretty handy when studying gravitational ...
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0answers
54 views

Gravity Concept Question [duplicate]

Thought experiment: Imagine the sun suddenly disappeared; lets say it some how transported to the edge of the observable universe.What will be the effects on the space-time? (1) What does General ...
4
votes
2answers
562 views

Is special relativity a special case of general relativity, qualitatively?

Since Einstein name his theory Special Relativity and General Relativity, there should be some expected relationship between them, particularly "Special Relativity" being a special case of the more ...
1
vote
1answer
68 views

Riemann curvature tensor notation in Wald

This question is entirely on tensorial notation in Wald's General Relativity. When specifying the properties of the Riemann tensor on pg39, he states: $R_{[abc]}^{\quad \ \ \ d} = 0$ and For the ...
2
votes
1answer
53 views

Graviton polarization in higher dimensions

It's not difficult to see that the graviton in $D$ spacetime dimensions has $(D-3)D/2$ polarizations. In $D=4$ there are two $\epsilon^{\pm}_{\mu\nu}$. What I find curious is that in $D=4$ I can ...
1
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1answer
48 views

Is the spacetime generated by isolated system always asymptotically flat?

I read a saying in wiki of asymptotically flat spacetime http://en.wikipedia.org/wiki/Asymptotically_flat_spacetime "In general relativity, an asymptotically flat vacuum solution models the exterior ...
1
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1answer
52 views

Does there exist a mathematically rigorous formulation of curved Hilbert Space?

The Hamiltonian is traditionally defined as \begin{align} H_{\text{flat}} = U^{\dagger}DU \end{align} where $D$ is a diagonal matrix with real eigenvalues and $U^{\dagger}U=I$ are the unitary ...
4
votes
1answer
81 views

How does the kinetic energy of quarks contribute to the mass of macroscopic objects?

As we know, most of the mass of ordinary matter comes from the kinetic energy of quarks. This means kinetic energy of quarks contributes to the mass of any object. However take a look at this ...
3
votes
1answer
81 views

Thought experiment: Tethered galaxies - to the extreme

If two rocks were tied together with a tight, absurdly long, non-elastic rope, and placed on planets at either end of Earth's observable universe - or beyond - What would happen? Is the structural ...
1
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0answers
36 views

Does a moving star have a larger gravitational pull? [duplicate]

A moving star's relativistic mass is larger than its rest mass. Is its gravitational pull larger? What about its inertial mass? Does it have larger inertial mass, keeping in mind that inertial mass ...
0
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1answer
31 views

Does general relativity have an effect of the frequency of light? [closed]

if a lightbeam is fired from space to earth is it blueshifted? I heard this happens with special relativity but not sure if it happens with genreal relativity
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3answers
92 views

Why does time slow down the closer you are to a mass?

When ever i look this up all I get is sites saying how its because general relativity says "-" why does it do it though? it is because there is more motion near gravity than further away? Or is it ...
2
votes
2answers
125 views

Textbook on classical E&M in curved spacetime

Can anyone recommend a good reference for classical electrodynamics that goes over electrodynamics in curved spacetime that doesn't assume much knowledge of GR -- that is it builds up the tensor ...
2
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3answers
269 views

A Conceptual Problem With the Field Equations of General Relativity

I have two questions: Suppose that we have an amount of energy in the form of a perfect fluid in the right hand side of Einstein field equations (energy momentum tensor), this will lead to a ...
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0answers
21 views

Problem books like I.E. Irodov for advanced physics [duplicate]

I really enjoyed doing problems from Irodov while learning introductory physics. But I am not able to find a book like that for Graduate level physics. Can you suggest me a book which has good (and ...
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1answer
53 views

Gravity in spacetime

Can the effect of gravity in spacetime be thought of as if nearby particles have a tendency to "align" their four velocity direction? I.e. "to point in the same direction".