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 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 ...
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1answer
175 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 ...
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1answer
81 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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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
40 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 ...
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42 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 ...
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56 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 ...
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1answer
42 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 ...
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1answer
47 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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33 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 ...
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3answers
104 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 ...
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52 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
45 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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30 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 ...
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1answer
99 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 ...
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1answer
132 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 ...
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69 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
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1answer
71 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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52 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 ...
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53 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 ...
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4answers
144 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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52 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 ...
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2answers
546 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 ...
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1answer
58 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 ...
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1answer
46 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 ...
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1answer
46 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 ...
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47 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 ...
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73 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 ...
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1answer
59 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 ...
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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 ...
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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
85 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 ...
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2answers
116 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 ...
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3answers
256 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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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
52 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".
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2answers
83 views

Invariant interval and gravity

Gravity is inversely proportional to the distance between objects. Do we use Euclidean distance or the invariant interval for that distance? Using the invariant interval makes everything a bit more ...
2
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1answer
175 views

Einstein and the existence of Black Holes

I have seen some papers claiming that Einstein said there is no Black Hole in the real world, here is a phrase from Einstein himself, see this arXiv preprint: The basic result of study is the ...
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341 views

Speed of light in general relativity

My question has a few parts concerning the speed of light in general relativity. Firstly, time changes in response to gravity and speed. Therefore, as gravity effects time in an area of space, should ...
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1answer
91 views

Geodesic curvature and Weyl transformations

The geodesic curvature is given by $$k=\pm t^a n_b\nabla_a t^b,$$ where $t^a$ is a unit vector tangent to the boundary of the string worldsheet and $n_a$ is an outward vector orthogonal to $t^a$. I ...
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3answers
54 views

Quantum Scales and the Flatness of Space-time

I know that on the smallest scales, general relativity predicts that space-time is flat. But I've also read that space-time can be described as a sort of "quantum foam" for distances smaller than the ...
3
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1answer
82 views

Was the firewall paradox resolved?

For quite sometime there has been a claim that the firewall paradox has been resolved (via lasers). For instance, http://global.ofweek.com/news/Lasers-to-solve-the-black-hole-information-paradox-9867 ...
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2answers
600 views

Why doesn't gravity bend everything equally?

If gravity is the curvature of spacetime it should bend everything equally. To clarify my point I would like you to imagine two scenarios. Think of a bird flying in the storm while the wind is blowing ...
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1answer
80 views

General relativity: gauge fixing

In his lectures professor Hamber said that the metric tensor is not unique, just like the 4 vector potential is not unique for a unique field in electrodynamics. Since the metric tensor is symmetric, ...
2
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2answers
339 views

If a photon has no mass, how can it be attracted by the Sun?

I read that the photon doesn't have mass, but my teacher says that the photon has mass because the sun can attract it (like in the experiments to prove the theory of relativity). I think that there ...
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37 views

What causes the unexpected change in acceleration for flybys of spacecraft?

If the vehicle is not operating on RTG, then thermal recoils of photons shouldn't be considered as in the case of PIONEER. Then what actually accelerate the spacecraft from expected value (expected by ...
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1answer
59 views

Do gravitational waves travel on geodesics in GR? If yes, why?

I think, the answer is probably yes, but it can be answered by somebody who knows GR much better than I do. In case of a positive answer, can we say that gravitational radiation will be bent around ...
3
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2answers
346 views

Which of these two textbook equations of geodesic deviation is correct?

My previous question Geodesic deviation on a 2-sphere - is this the right track? got shot down as “off topic”, so I'm having a second stab at it. Misner et al's Gravitation (p34) gives the geodesic ...
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Textbook disagreement on geodesic deviation on a 2-sphere

Apologies if I have this completely wrong (and for the general long-windedness). I've searched online but can't find anything helpful/relevant. I'm trying to use the geodesic equation ...
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1answer
34 views

Junction conditions in GR including electromagnetism

I have recently learned about the Israel junction conditions in GR (as explained in for example Gravitation by MTW). I then tried to generalize it when including Electromagnetism, ie matching two ...