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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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
72 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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0answers
91 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
66 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
182 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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48 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
423 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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2answers
103 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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1answer
178 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
196 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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1answer
252 views

Could strings be geons?

Is it possible that string theory strings are geons? This may be an overly speculative or naive question, but is there an obvious reason why not? Both strings and geons seem to have roughly the same ...
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2answers
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Is dark matter repulsive to dark matter? Why?

I think I saw in a video that if dark matter wasn't repulsive to dark matter, it would have formed dense massive objects or even black holes which we should have detected. So, could dark matter be ...
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98 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 ...
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1answer
139 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
261 views

What is the radius of convergence of the Fefferman-Graham expansion?

There is this general result that for any metric $ds^2$ that is asymptotically $AdS_{d+1}$, then there is a coordinate system in which $$ ds^2 = \frac{1}{r^2}(dr^2 + g_{ij}(r,x^k)dx^i dx^j) $$ where ...
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0answers
108 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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1answer
74 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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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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5answers
167 views

Can the equivalence principle be shown to follow from special relativity?

Einstein showed in various papers that the energy content of a body was a measure of its inertial mass. If you increase the internal energy of a system while keeping the center of energy at rest, its ...
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0answers
62 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
1k 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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2answers
193 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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1answer
150 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
162 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
300 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
139 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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0answers
38 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
43 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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2answers
479 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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3answers
350 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
39 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 ...
3
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1answer
968 views

Are there any good video lectures for learning general relativity at the level of Hobson?

Before answering, please see our policy on resource recommendation questions. Please try to give substantial answers that detail the style, content, and prerequisites of the book or paper (or ...
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2answers
173 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 ...
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1answer
75 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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1answer
232 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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2answers
998 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
161 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
79 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 ...
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2answers
710 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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0answers
160 views

What are the current experimental restrictions of the possible speeds of gravitation?

Somewhere I read that the Hulse-taylor binary pulsar can not differentiate between competing theories assuming different speeds of gravity. Is it mathematically true in general, that the orbital decay ...
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1answer
170 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
571 views

Mistake in Briefer History of Time by Stephen Hawking [closed]

I was reading A Briefer History of Time by Stephen Hawking and Mlodinow. I found something silly. On page 36 at the bottom, it says the following : If, say, the sun suddenly disappeared, Maxwell's ...
2
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1answer
71 views

Specific problems with the quadrupole formulation of gravitational radiation

the quadrupole formula has some counterintuitive consequences, when analysing the power output averaged over a period $$ P = \langle \frac{d^3 Q_{ij}}{dt^3} \frac{d^3 Q_{ij}}{dt^3} \rangle $$ ...
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1answer
224 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, ...
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0answers
162 views

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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2answers
407 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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1answer
88 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 ...
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1answer
560 views

Justification for new theories of Particle Physics and General Relativity

In reference to arxiv:1212.4893v3 and arxiv:1206.5078v2 papers of Ma and Wang, they have proposed new theories in particle physics, the weakton model where quarks and leptons are formed using these ...
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158 views

Is there a general stress-energy tensor for vector fields?

I've been reading about scalar fields in the context of general relativity, and I found this page: https://en.wikipedia.org/wiki/Stress-energy_tensor#Scalar_field. It says that the stress-energy ...
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182 views

What is the metric of Vaidya black-hole horizon?

The metric of a Vaidya black hole in outgoing/retarted null coordinates are $$ds^2=-\left(1-\frac{2m(u)}{r^2}\right)du^2-2dudr+r^2\Big(d\theta^2+\sin^2\theta d\phi^2 \Big)$$ The eveolving horizon ...