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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Curvature of Conical spacetime

Inspired by: Angular deficit The 2+1 spacetime is easier for me to visualize, so let's use that here. (so I guess the cosmic string is now just a 'point' in space, but a 'line' in spacetime) Edward ...
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2answers
388 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
2
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0answers
47 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
34 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
40 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
96 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
928 views

How do we determine the temperature of a Black Hole?

How do we determine the temperature of a Black Hole? Since we cannot see a Black Hole, which I presume, is because it absorbs light, would it not also prevent radiation from escaping, making ...
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2answers
162 views

Changing vector basis in AdS$_3$

I have AdS${}_3$ given as a surface embedded in a 4 dimensional pseudo-Riemannian space $$x^2+y^2-u^2-y^2=-l^2$$ With metric: $$ds^2=dx^2+dy^2-du^2-dv^2$$ I have Killing vectors of that space ...
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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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1answer
49 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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1answer
41 views

Robertson-Walker metric and stable orbits

The RW metric is defined using 4 spatial dimensions, but stable planetary orbits require 3 spatial dimensions. Does this indicate a problem with the assumption of the RW metric to describe the cosmos? ...
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0answers
28 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
98 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
128 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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2answers
1k views

Value of the Hubble constant over time

There is something I don't understand about the Hubble "constant" H, as it seems to clump two concepts together that I can't quite unify in my head. On the one side, we have $$V = D H$$ which means ...
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4answers
910 views

Can general relativity be completely described as a field in a flat space?

Can general relativity be completely described as a field in a flat space? Can it be done already now or requires advances in quantum gravity?
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1answer
110 views

Wave Packet in Curved Spacetime

It is known that the classical equation of motion for a scalar field wave packet on a curved spacetime background gives the geodesic trajectory (the e.o.m. is $(\nabla_\mu \nabla^\mu + m^2) \Phi=0$). ...
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1answer
225 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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4answers
2k views

The bigger the mass, the more time slows down. Why is this?

If I were to stand by a pyramid, which weighs about 20 million tons, I would slow down by a trillion million million million of second. Don't know if that's exactly right, but you get the point. Also, ...
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2answers
1k views

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 ...
2
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0answers
65 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
67 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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2answers
504 views

Is general relativity holonomic?

Is it meaningful to ask whether general relativity is holonomic or nonholonomic, and if so, which is it? If not, then does the question become meaningful if, rather than the full dynamics of the ...
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0answers
98 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
51 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
45 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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3answers
653 views

Is gravitational time dilation different from other forms of time dilation?

Is gravitational time dilation caused by gravity, or is it an effect of the inertial force caused by gravity? Is gravitational time dilation fundamentally different from time dilation due to ...
3
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0answers
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
141 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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5answers
148 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
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 ...
4
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2answers
545 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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3answers
1k views

Rocky Planet in the center of System [duplicate]

We all know that mostly stars are at the center of planetary systems, but is it possible that instead of star there was a rocky planet in the center with stars (and other planets and moons) orbiting ...
2
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2answers
114 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
57 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
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1answer
123 views

Trajectory of a photon around a Schwarzschild black hole?

Consider a photon coming from the infinity in a unbounded orbit to a Schwarzschild black hole (Schwarzschild radius $r_{s}$) (see this for illustration). Its impact parameter is $b$ and its distance ...
4
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1answer
72 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 ...
2
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1answer
45 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

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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1answer
95 views

GR exercise: falling particles on earth's surface

I'm having some trouble with Exercise 5.1 in Shapiro's BH,WD&NS book, which goes as follows: Consider two particles of mass $m$ at distance $r$ and $r+h$, such that $h\ll r$, on the same ...
3
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1answer
56 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 ...
7
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1answer
386 views

Surface gravity of Kerr black hole

I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand. Firstly, the metric is given by ...
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0answers
35 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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3answers
84 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 ...
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
2
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2answers
338 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 ...
2
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3answers
254 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 ...
3
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1answer
368 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 ...