Questions tagged [general-relativity]

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.

2,367 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
15 votes
0 answers
399 views

Derivatives of distributions in general relativity

I am having some trouble when trying to reproduce some calculations involving the description of distributions (mostly used in spacetime junction conditions). I am trying to reproduce the ...
user avatar
14 votes
1 answer
373 views

In realistic gravitational collapse, can we have an absolute horizon without a trapped surface?

In gravitational collapse, it seems that there is no close or simple logical relationship between the formation of an event horizon (absolute horizon) and formation of a trapped surface (which implies ...
user avatar
12 votes
0 answers
589 views

What are Galileons good for?

Lately I've seen many papers (for example "The galileon as a local modification of gravity"; 292 total hits on the arXiv) on types of field theories known as Galileons, and I'm wondering what the ...
user avatar
11 votes
0 answers
315 views

Holonomy group of Schwarzschild spacetime, other interesting examples?

I'm teaching myself a little about holonomy groups in the context of general relativity. This paper by Hall and Lonie classifies a lot of the possibilities for simply connected spacetimes in 3+1 ...
user avatar
11 votes
0 answers
2k views

How to show the Gauss-Bonnet term is a total derivative?

It is well-known that the Gauss-Bonnet term $$\mathcal L_G =R^2 -4 R_{\mu\nu}R^{\mu\nu}+R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\tag 1$$ do not contribute to equations of motion when adding it to the ...
user avatar
11 votes
1 answer
288 views

gravitational convergence of light

light has a non-zero energy-stress tensor, so a flux of radiation will slightly affect curvature of spacetime Question: assume a flux of radiation in the $z$ direction, in flat Minkowski space it ...
user avatar
10 votes
0 answers
290 views

How to perform a derivative of a functional determinant?

Let us consider a functional determinant $$\det G^{-1}(x,y;g_{\mu\nu})$$ where the operator $G^{-1}(x,y;g_{\mu\nu})$ reads $$G^{-1}(x,y;g_{\mu\nu})=\delta^{(4)}(x-y)\sqrt{-g(y)}\left(g^{\mu\nu}(y)\...
user avatar
  • 3,441
10 votes
0 answers
236 views

Can you put the Spin Connection in block diagonal form? (to be applied to the Atiyah-Singer theorem)

I'm following the notes by Freed about the Dirac Operator. In section 5.4, equation (5.4.25-27), he makes the following claim about the Dirac operator. In different notation than he is using, he is ...
user avatar
  • 656
10 votes
0 answers
1k views

Variation of the Einstein-Hilbert action in D dimensions without the Gibbons-Hawking-York term

Consider the standard Einstein-Hilbert action in $D \ne 2$ dimensions spacetimes : \begin{equation} S_{EH} = \frac{1}{2 \kappa} \int_{\Omega} R \; \sqrt{- g} \; d^D x, \end{equation} where $\Omega$ is ...
user avatar
  • 6,696
10 votes
1 answer
943 views

Escape velocity for Schwarzschild metric

I can't fill in the gaps in my solution to this and assistance or a reference would be appreciated. The question begins with the straightforward derivation of the EoM for a massive particle orbiting ...
user avatar
  • 214
10 votes
0 answers
185 views

Candidates for holographic QFT of 4D Einstein gravity

If we are to believe that holographic principle holds over a wide number of dimensions, and gravitational theories, but specially, those that are relevant to our universe, then there must be some 3D ...
user avatar
  • 14k
10 votes
0 answers
336 views

Significance for LQG of Sen's result on entropy of black holes?

Sen 2013 says, ...we apply Euclidean gravity to compute logarithmic corrections to the entropy of various non-extremal black holes in different dimensions [...] For Schwarzschild black holes in ...
user avatar
9 votes
0 answers
273 views

Basic questions on the PPN formalism in General Relativity

I'm trying to learn about testing modified gravity using the PPN formalism. I have several textbooks that I am reading through (including Clifford Will's book), and have some basic questions on the ...
user avatar
  • 1,619
9 votes
0 answers
500 views

What are problematic issues of quantum field theory in curved spacetime, when accepting semiclassical limitation?

The question is inspired from the answer to Is a QFT in a classical curved spacetime background a self-consistent theory? (I am going to reference this link as "The Q" to avoid confusion). As far as ...
user avatar
9 votes
0 answers
354 views

View of the sky from inside a black hole

Consider an observer located at radius $r_o$ from a Schwarzschild black hole of radius $r_s$. The observer may be inside the event horizon ($r_o < r_s$). Suppose the observer receives a light ray ...
user avatar
  • 1,274
9 votes
0 answers
214 views

Radiative equilibrium in orbit of a black hole

According to Life under a black sun, Miller's planet from Interstellar, with a time dilation factor of 60,000, should be heated to around 890C by blue-shifted cosmic background radiation. How they ...
user avatar
9 votes
0 answers
518 views

Will a black hole cause scattering of a gravitational wave?

In my GR textbook, it states that gravitational waves can undergo interference but not scattering. I am just starting the chapter on linearised gravity concepts (weak field approximation) and my ...
user avatar
9 votes
0 answers
275 views

What really are exotic supersymmetric black holes?

I have just read (in the black holes chapter 14 on p244 of this book Ref.1) that in string theory, when one adds an (electric?) charge $Q$ to a static black hole, one can arrive at an exotic ...
user avatar
  • 9,187
9 votes
2 answers
346 views

How will two equal discs, rotating with equal but opposite angular velocities and put on top of each other affect the spacetime "surrounding" them?

In this article the Ehrenhaft paradox is described. You can read in it that, according to Einstein's General Relativity (to which this paradox contributed), the spacetime around a rotating disc is non-...
user avatar
9 votes
1 answer
988 views

Can tachyons escape the gravitational pull of a classical black hole?

Anything that crosses the event horizon of a black hole cannot escape the pull since it has crossed the Schwarzschild radius and thus, the escape velocity is greater than the speed of light, and since ...
user avatar
  • 1,063
8 votes
0 answers
164 views

What is the difficulty in extending geometrodynamics to non-abelian fields?

In an attempt to widen my own horizons I've decided to educate myself in Wheeler's Geometrodynamics. In the so-called "already unified theory" one can essentially reproduce an electromagnetic field ...
user avatar
  • 2,507
8 votes
0 answers
356 views

What is the Chandrasekhar-Friedman-Schutz (CFS) instability, exactly?

I am confused as to what the Chandrasekhar-Friedman-Schutz (CFS) instability is, exactly. It seems to partially refer to this paper (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.24.611) ...
user avatar
  • 10.9k
8 votes
0 answers
480 views

What methodologies present in MTW's Gravitation are outdated and why?

MTW's Gravitation is regarded by many universities as the standard graduate-level book on General Relativity. However, is the methodology of the book of contemporary character? The cosmology part of ...
8 votes
0 answers
278 views

The color of deep space background of an arbitrary universe

While writing my notes on cosmology in general relativity and the Olber's paradox, I was wondering about the color of the deep background of space. Our universe is mostly black because light didn't ...
user avatar
  • 6,696
8 votes
0 answers
194 views

Metric transformation, polygons and gravitons

I'm trying to understand the paper by Hitchin called: ''Polygons and gravitons". I'm stuck at page 471. At this point, he does some computations and obtains a metric: $$ \gamma dz d\bar{z}+\gamma^{...
user avatar
8 votes
1 answer
730 views

Conservation of Komar mass

The definition of Komar mass in GR is associated with one asymptotically flat end. However, a hypersurface may contain more than one end, such as the spacelike Einstein-Rosen bridge in Kruskal ...
user avatar
  • 1,059
8 votes
0 answers
229 views

Is there a null incomplete spacetime which is spacelike and timelike complete?

Geodesic completeness, the fact we can make the domain of the geodesic parametrized with respect an affine parameter the whole real line, is an important concept in GR. Especially, because the lack of ...
user avatar
  • 1,999
8 votes
0 answers
3k views

How to prove that Weyl tensor is invariant under conformal transformations?

I need to verify that the solution for vanishing Weyl tensor is conformally flat metric $g_{\mu\nu} = e^{2\varphi}\eta_{\mu\nu}$. The most convenient way to show this is to prove that Weyl tensor is ...
user avatar
8 votes
0 answers
686 views

Questions on Penrose's paper - Conformal Treatment of Infinity

I have several questions. Perhaps it would be better to separate them into different posts. However, given their relative closeness to each other, I think putting it all in one place would be better. ...
user avatar
  • 20.6k
8 votes
0 answers
221 views

Implications of Unruh-inertia to theories of gravity

If it turns out to be true that the galaxy rotation curves can be explained away by Unruh modes that become greater than the Hubble scale at accelerations around $10^{-10} m/s^2$ as proposed in here, ...
user avatar
  • 14k
8 votes
1 answer
283 views

Observational evidence for wormholes, or not?

The Wikipedia article on wormholes claims: Researchers have some observational evidence for wormholes, and the equations of the theory of general relativity have valid solutions that contain ...
user avatar
7 votes
0 answers
100 views

Can the Lorentz force equation in curved spacetime be derived from the Einstein-Maxwell equations?

Given the Einstein field equations, $$R_{\mu\nu} - \frac{1}{2}R g_{\mu\nu} = \kappa T_{\mu\nu}$$ that imply in particular that $\nabla_\mu T^{\mu\nu}=0$, one can show, using the explicit form of $T^{\...
user avatar
  • 695
7 votes
0 answers
126 views

Does vibration in molecules cause meaningful local differences of time dilation in matter?

I learn through confusion, and something about molecular structure still very much confuses me. A vibrating clock will ultimately run slower than your wristwatch, because of, for one, kinematic time ...
user avatar
7 votes
0 answers
388 views

Solving Maxwell equations on curved spacetime

I have difficulties to understand how to solve the Maxwell equations on curved spacetime. I want to solve the equations in the weak regime $g_{\mu\nu}=\eta_{\mu\nu}+h{\mu\nu},~ h_{\mu\nu}\ll 1$ ...
user avatar
7 votes
0 answers
328 views

Definition of gravity path integral?

In a non-abelian gauge theory there is a "fundamental" gauge field $A_\mu^a$ with gauge index $a$ often called connection. Although $ A_\mu^a$ is not gauge invariant, gauge invariant quantities can be ...
user avatar
  • 282
7 votes
0 answers
331 views

Aren't black holes required to exist forever in our frame of reference instead of evaporating?

I know that for an observer far away, nothing ever crosses a black hole horizon (due to time dilation), while in the frame of reference of a falling observer the horizon is nothing special on its way ...
user avatar
7 votes
0 answers
177 views

Relativistic rotational squeezing?

I would like to consider a sphere rotating at very high angular speeds, such that the speed in its equator would be relativistic. This is very similar to Ehrenfest paradox situation, except that ...
user avatar
  • 3,697
7 votes
0 answers
1k views

Energy-Momentum Tensor of a Gravitational Wave

In radiation gauge ($\gamma=0$), the Einstein field equation in vacuum for a perturbation $\gamma_{\mu\nu}:=g_{\mu\nu}-\eta_{\mu\nu}$ is given by $$ \boxed{ \partial^\alpha\partial_\alpha \gamma_{\mu\...
user avatar
  • 2,084
7 votes
0 answers
714 views

Why is the Ricci tensor diagonal for isotropic spacetime?

I'm reading Zee's Einstein Gravity in a Nutshell and while calculating the Ricci tensor for FRW spacetime he claims that because the spacelike slices of constant $t$ are rotationally invariant, the ...
user avatar
  • 740
7 votes
0 answers
195 views

What is the state-of-the-art on spacelike singularities in string theory?

What lessons do we have from string theory regarding the fate of singularities in general relativity? What happens to black hole singularities? What happens to cosmological singularities? Which ...
user avatar
7 votes
0 answers
407 views

Asymptotic Invariants in General Relativity

I was trying to understand Witten's proof of the Positive Energy Theorem in General Relativity by reading the original argument given by Witten. I am comfortable with the overall argument, but I would ...
user avatar
7 votes
1 answer
211 views

Graviton detector thought experiment

I was recently thinking of a thought experiment: Assumptions Graviton detectors can exist The equivalence principle will hold in the final theory of quantum gravity We can accelerate the graviton ...
user avatar
  • 1,147
7 votes
1 answer
276 views

Charged versus rotating black holes as different kinds of wormholes

I've heard that a maximally extended charged black hole can be a traversable wormhole to the same universe whereas a maximally extended uncharged rotating black hole can only be a wormhole to ...
user avatar
  • 24.6k
6 votes
0 answers
96 views

Is GR the only theory in physics which cares about absolute energy?

In my QFT course, they justify dropping the vacuum energy as 'physics only cares about relative energies except for GR in the stress-energy tensor'. Is this strictly true?
user avatar
  • 2,282
6 votes
0 answers
92 views

Angular momentum of vacuum solution in Einstein gravity

In Strominger's "Lecture Notes on Infrared Structure of Gravity", page 38, he mentioned about how part of this whole mess about "vacuum degeneracy" (classically, i.e. in the sense ...
user avatar
  • 1,405
6 votes
0 answers
78 views

Is classical Kaluza Klein theory stable or not?

Set Up In the original classical Kaluza Klein theory, you have a $d+1$ dimensional manifold where one space dimension is a circle $S^1$. In the "low energy limit," none of the metric ...
user avatar
  • 10.9k
6 votes
0 answers
389 views

Weyl transformation vs diffeomorphism; conformal invariant vs general in/covariant

Background info: My understanding: 1. Weyl transformation is a local rescaling of the metric tensor $$ g_{ab}\rightarrow e^{-2\omega(x)}g_{ab} $$ A theory invariant under this Weyl transformation is ...
user avatar
6 votes
0 answers
194 views

Question about the Newtonian limit of general relativity

I ran into something peculiar while attempting to carefully derive the Newtonian limit of general relativity, specifically for the geodesic equation. To set it up, we assume that the curve $q:[a,b]\...
user avatar
6 votes
0 answers
136 views

Resource Recommendation for black hole metrics in General Relativity

In classical textbooks for GR, Schwarzschild and Kerr spacetimes are adequately described. In which books or articles, it is mostly believed that Reissner–Nordstrom, Kerr–Newman, Schwarzschild–de ...
6 votes
0 answers
568 views

Auto-parallel Transport or Principle of Extremum Action?

In an affinely connected spacetime with a metric compatible connection, the equation of the curve in which the tangent vector at each point is the result of the parallel transport of every tangent ...
user avatar
  • 19.2k

1
2 3 4 5
48