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.

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Do any quantum gravity theories deal with closed timelike curves?

As far as I'm aware, there are no quantum gravity theories that deal directly with closed timelike curves. Some of them (like canonical quantum gravity, causal dynamical triangulation and loop quantum ...
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On the finiteness of quantum gravity$.$

Consider naïve quantum gravity, defined by $$ Z=\int e^{-\frac{1}{\hbar}\int R}\mathrm dg $$ where $R$ denotes the Ricci scalar, and $\mathrm dg$ a path integral over all metrics. I have set $G_N=1$ ...
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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 ...
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1answer
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Deriving the Poisson bracket relation of the Ashtekar variables

I'm trying to figure out how to calculate the orthogonality of Ashtekar variables with respect to the ADM hypersurface metric and conjugate momentum. $$\{{A_a}^i(x), {E^b}_j(y)\} = 8 \pi \beta \delta^...
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Do the Planck voltage and the Planck current have a natural physical interpretation in classical general relativity?

Most Planck units are a product of powers of all three of $\hbar$, $c$, and $G$, so we will not be able to fully understand their physical significance until we have a full theory of quantum gravity. ...
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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 ...
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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 ...
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534 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 ...
11
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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 ...
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217 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 ...
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0answers
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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 contributes to equations of motion when adding it to ...
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1answer
275 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 ...
9
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0answers
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Does the Gibbons-Hawking boundary action have an anomaly inflow interpretation?

The Einstein-Hilbert action on a manifold $M$ with boundary is $$\frac{-1}{16\pi G}\int_M d^n x \sqrt{-g} R +\frac{1}{8\pi G} \int_{\partial M} d^{n-1}x \sqrt{|h|} K$$ where $K$ is the extrinsic ...
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239 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 ...
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Does a classical charge naturally have spin in a non-flat FLRW universe?

I was recently reading a paper https://arxiv.org/abs/0912.0225 which describes Coulomb's law in a closed universe. I've seen the argument from several sources that the total electric charge in a ...
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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 ...
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991 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 ...
9
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1answer
605 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 ...
9
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317 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 ...
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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 ...
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1answer
791 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 ...
8
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How does the non-degeneracy of the metric imply that gravity is not fundamental?

In his General Relativity notes, on page 149, David Tong remarks that when we look for solutions to Einstein's equations, we can't just take any metric, such as $g_{\mu \nu} = 0$; we must pick one ...
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Cosmological consequences of the mass-energy content of gravitational waves

This paper published in 1969 indicates that a majority of the mass-energy of the universe may be contained in gravitational waves: "Turning next to phenomena on a galactic scale, we find it ...
8
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174 views

QFT in Curved Spacetime - Commutation Relations for Annihilation Operators

I am currently learning about QFT in curved spacetime using these notes. Given a subspace $S_p$ of positive frequency solutions to the Klein-Gordon equation, we defined the corresponding ...
8
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0answers
144 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 ...
8
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266 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) ...
8
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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 ...
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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 ...
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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 ...
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178 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^{...
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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 ...
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482 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 ...
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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 ...
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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. ...
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214 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, ...
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1answer
259 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 ...
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1answer
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Weak gravity limit of (Einstein-Hilbert + matter) action

The problem Consider the following euclidean action $$ S_E = - \int_{\mathcal{M}} d^4x \sqrt{g} \left [\frac{R}{2 \kappa} +\mathcal{L}_M \right ] + S_{GHY},$$ where $S_{GHY} = -\int_{\partial \...
7
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1answer
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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 ...
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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 ...
7
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0answers
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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 ...
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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 ...
7
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2answers
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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-...
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1answer
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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 ...
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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]\...
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273 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 ...
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de-Sitter spacetimes

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 ...
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Black hole merger for a distant observer

Recently, the LIGO detections of the gravitational waves from black hole merger events have rightly caused a lot of media attention. There is something I do not quite understand, however. In the ...
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448 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 ...
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0answers
283 views

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

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 ...
6
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0answers
223 views

General Relativity as a Special Relativistic Field Theory

In this question, I want to consider only the classical case. I have seen the statement that general relativity can be considered as a spin-2 field living on a Minkowski background. In that case, you ...

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