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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A dictionary of string - standard physics correspondences

Motivated by the (for me very useful) remark ''Standard model generations in string theory are the Euler number of the Calabi Yau, and it is actually reasonably doable to get 4,6,8, or 3 ...
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571 views

What different approximations yield Gravitoelectromagnetism and Weak Field Einstein Equations?

This question is inspired by this answer, which cites Gravitoelectromagnetism (GEM) as a valid approximation to the Einstein Field Equations (EFE). The wonted presentation of gravitational waves is ...
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196 views

Does the spin of a particle change if observed from an accelerating reference frame?

If we consider a spin-$\frac12$ particle at rest in the absence of any potentials, we can use the Pauli spin operators and an associated basis to describe the observable. Let's arbitrarily choose the ...
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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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210 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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183 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 ...
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148 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 ...
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133 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 ...
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117 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 ...
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267 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 ...
6
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104 views

Can some components of metric be Finslerian while the others be Riemannian?

A Finsler metric reduces to a Riemann metric in case it loses its dependence on velocities. Now, my question is this: Can we have a Finsler metric in which some components of the metric have velocity ...
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96 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 ...
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376 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 ...
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154 views

What do we learn from gravity in three spacetime dimensions?

The last decades there has been a lot of research going on in the the area of three dimensional gravity. The motivation, I understand, is threefold: Whereas gravity is not perturbatively ...
6
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154 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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190 views

How to obtain the free energy of the canonical ensemble in Euclidean general relativity?

If the gravitational field couples with matter fields, such as a charged scalar field, I know the partition function of the grand canonical ensemble naturally relates to the path-integral expression ...
6
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158 views

Do semiclassical GR and charge quantisation imply magnetic monopoles?

Assuming charge quantisation and semiclassical gravity, would the absence of magnetically charged black holes lead to a violation of locality, or some other inconsistency? If so, how? (I am not ...
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176 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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39 views

In a perturbative FRW cosmology, why do constant-density hypersurfaces define a good gauge?

It appears to be common in the discussion of perturbative FRW cosmologies to choose a gauge using hypersurfaces for special values of some quantity, like surfaces of constant density $\rho$, constant ...
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222 views

Penrose diagram for spacetime which flows to $AdS_{2}$ at infinity

Consider I have the following 2 dimensional spacetime $(t,z)$: $$ds^2=\frac{4}{z^{2}}\left(1+\frac{1}{z}\right)^{-1}(-dt^{2}+dz^{2}).\tag{1}$$ When $z\rightarrow \infty$ we have ...
5
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119 views

BTZ Black Hole Central Charge and Conformal Weight

I have been trying to reproduce a calculation (equation 4.12) in this paper http://arxiv.org/pdf/1107.2678v1.pdf by Carlip reviewing the derivation of the effective central charge of the BTZ Black ...
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200 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 ...
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Further explanation of the Penrose Conjecture

I'm currently a third year maths undergrad, writing a dissertation on the application of minimal surfaces in space. I have recently come across the Penrose Conjecture that the mass of a spacetime is: ...
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133 views

Why can apparent horizon be computed based on its local geometry?

Why can apparent horizon be computed based on its local geometry? In the paper titled Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity by Hubert L. Bray, has been ...
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182 views

Euclidean black hole extrinsic curvature

I have read that the extrinsic curvature at the horizon of a euclidean black hole is zero? Does anybody know how this can be shown?
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265 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. ...
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173 views

Singularity and Black Hole Complementarity

When looking at a (eternal) Schwarzschild Black Hole, we may identify two worlds. The region $R_1$ (right) - our world -, and the region $R_2$ (left) - an other world. The "black hole interior" ...
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208 views

Gravitational redshift of Hawking radiation

How can Hawking radiation with a finite (greather than zero) temperature come from the event horizon of a black hole? A redshifted thermal radiation still has Planck spectrum but with the lower ...
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61 views

How does Lorentz Contraction apply to the edge of a spinning disk and is Pi still constant?

This may seem like a dumb question, as I'm not really a physicist, but here it goes. So, π (3.14...) is the number of diameter distances required to equal the circumference of a 2D disk. Relativity ...
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184 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 ...
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71 views

General theorems on tachyon propagation?

I was reading the quite nice answer of QMechanic on the topic of compact support tachyon fields not propagating faster than light, but this case is a rather simple one, free scalar field in flat ...
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65 views

Question about $\alpha-$plane in twistor theory

In twistor theory, given the complexified Minkowski space $CM$ and the projective twistor space $PT$, an $\alpha-$plane is defined as the correspondence in $CM$ wit a point $Z \in PT$. But I found ...
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109 views

Angle sum of triangle in Schwarzschild solution

Curvature of space is often intuitively explained as angles of a triangle not adding up to 180 degrees. My questions concerns that. Suppose you have a perfectly spherical star of uniform density - so ...
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86 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 ...
4
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82 views

Are there relativistic theories with spacetime modelled on $\mathbb C^4$ rather than real Minkowski space $\mathbb R^4$?

Does anybody know of references to theories where relativity & spacetime is modelled on a (complex/Kähler) manifold which is locally diffeomorphic to $\mathbb C^4$ rather than $\mathbb R^4$, hence ...
4
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278 views

Tricks for Computing Riemann Curvature Tensor with Levi-Civita connection

I am new to differential geometry, so far it seems to me that computing the Riemann tensor tends to be a rather tedious task, I wanted to know whether there are some tricks that I am missing. In ...
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86 views

General relativity from helicity 2 massless field theory by using Deser's arguments

Recently I have discovered the method of constructing of GR from massless field with helicity 2 theory. It is considered here, in an article "Self-Interaction and Gauge Invariance" written by Deser S. ...
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64 views

Confinement of charged tachyons in AdS spacetime

It is well known that the negative cosmological constant of AdS spacetime can act like a confining potential. That is, in contrast to asymptotically flat spacetime, in an asymptotically AdS spacetime ...
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154 views

Lie derivative of Dirac Delta

In the setting of general relativity, I came across a source term of the wave equation of the following form: $$ \frac{1}{\sqrt{q}}\,\delta^{(3)}(p-\gamma(t)) $$ where $p\in M$ is a point in our 4d ...
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167 views

Dirac equation in curved spacetime - found second derivatives of the metric, violation of the principle of equivalence?

I am working on the Dirac equation on curved spacetime. A Foldy-Wouthuysen transformation was applied to obtain the semiclassical limit of the equation to study the dynamics of the spin of the ...
4
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223 views

How to draw the Poincaré patch of ${AdS_3}$?

My main reference for this question are these notes (maximally symmetric spaces.pdf) by Kurt Hinterbichler. I'm using Global Coordinates: \begin{align} x^0&=\sec{R}\cos\tau\\ ...
4
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321 views

The difference between an apparent horizon and event horizon?

I'm currently writing a project on minimal surfaces and general relativity - however I don't understand the difference between the apparent and event horizon? They ultimately both seemed to be defined ...
4
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98 views

Klein Gordon eq. expressed with Killing fields

I have a question on the reformulation of the Klein Gordon equation in terms of Killing fields. Suppose we have a static spacetime with timelike Killingfield $\xi^{\mu}$ (e.g. Schwarzschild). Then ...
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261 views

Superspace as the Hilbert Space for Quantum Gravity

Let $\mathcal{A}$ be the Ashtekar connection. Since $^{(3)}g_{AB}=i\frac{\delta}{\delta\mathcal{A}^{AB}}$ (see R. Penrose, 2004: Road to Reality. Vintage Books, 1136 pp.), the Ashtekar connection, in ...
4
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118 views

Timelike Loop Spaces as Projective Null Twistor Spaces

Let $\mathcal{M}$ be a spacetime, and let $\Omega\mathcal{M}$ denote the loop space of the spacetime. My idea is that the set of all closed timelike curves of $\mathcal{M}$ forms the projective null ...
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130 views

Some questions about spacetime topology, causality structures and other GR businesses

1) What are the exact conditions required for the canonical transformation? Most papers just assume away with global hyperbolicity, but is there a more general condition for it? "Quantum gravity in ...
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One more time about Nordstrom theory

Wikipedia says that Nordstrom theory with equations of motion of the test particle $$\tag{1} \frac{d (\varphi u_{\alpha})}{d \tau} = \partial_{\alpha} \varphi $$ and field equation $$\tag{2} \varphi ...
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Calculating Forces via Feynman diagrams?

How would one go about calculating forces that test objects feel using Feynman diagram methods? For example, say we have a massive object in GR so that the metric takes on the standard ...
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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 ...
4
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260 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 ...