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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Projector and delta function on a cycle $\Sigma$ of a manifold $\mathcal{M}_6$

In the paper ``Hierarchies from Fluxes in String Compactifications'' by Giddings, Kachru and Polchinski, the following example is considered for a localized source that may have negative tension (my ...
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Weinberg-Witten theorem and Landau pseudotensor, or how QFT can make prediction about GR

Weinberg-Witten theorem states that there isn't Poincare covariant stress-energy tensor for massless fields with helicity more than $1$. The only example of such higher helicity field is graviton. ...
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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 ...
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Maxwell's equation in curved spacetime - how come? And experimental evidence?

I'm trying to understand the generalization of Maxwell's equations to curved spacetime. In FLAT (Minkowski) SPACETIME: If we define the "four-potential" as $$\ ...
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Can I hide a charge behind a black hole?

Suppose that you are standing on one side of a black hole. I'm standing directly opposite you, on the other side of the BH, and I'm holding a charged particle. Is it possible for us to be positioned ...
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How does Space-Time Cloak work?

Well, scientists have achieved Spacetime cloaking to make events fully disappear. Currently, it works only for a trillionth of a second, but here's real-world scenario from linked page: In theory, ...
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Does relativistic glider violate principle of equivalence?

The relativistic glider proposed can slow down the fall of an object in gravitational field. Will this violate the principle of equivalence which says that one cannot distinguish between free falling ...
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Time functions in general relativity

In my general relativity notes a function $f$ is called time function, if $\nabla f$ is time-like past-pointing. Say that we are in Schwarzschild spacetime and I want to check if $f=t$ is a time ...
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Movie Interstellar - Followup Question to Escape Velocity

Continuing the discussion on this thread: Movie Interstellar - Question about Escape Velocity The movie Interstellar shows people on a water planet where time is dilated so much that 1 hour is equal ...
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No-hair theorems for naked singularities?

For black holes, we have no-hair theorems that say, under certain assumptions about the matter fields, that they are uniquely characterized by just a few parameters. Are there any such theorem for ...
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Does Hawking radiation need an apparent horizon and when does it switch on during stellar collapse?

I've read that Hawking radiation is implicitly linked with the existence of an apparent horizon (1). This seems a slightly less onerous than linking Hawking radiation with a genuine bona fide event ...
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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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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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Are closed timelike curves generic feature of ANEC-violating stress-energy tensor?

Kip Thorne has shown that in order to create closed timelike curves (CTCs), one needs stress-energy tensor $T^{\mu\nu}$ that violates averaged null energy condition (ANEC). Will $T^{\mu\nu}$ with ...
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Parity invariance of Einstein-Hilbert Lagrangian

How can we show that the Einstein-Hilbert action is Parity invariant? $$ S_{EH}=\int \sqrt{-g}R d^4x $$
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Is the “Force” of Gravity Simply Hamilton's Principle on a Curved Spacetime?

It's my understanding that General Relativity abstracts away the concept of gravity as a force, and instead describes it as a feature of spacetime by which massive objects cause curvature. Then it ...
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Should a radiation-filled Universe be scale invariant?

Imagine a spatially flat Universe, without cosmological constant, filled only with EM radiation. As Maxwell's equations without charges or currents are scale invariant then should this Universe be ...
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Asymtotically flat spacetime applicable for spacetimes which are not diffeomorphic to $\mathbb{R}^4$

I wanted to investigate changes on a compact 4-manifold $M$. More specifically it is the K3-surface. I follow a paper by Asselmeyer-Maluga from 2012. The idea there was to make sure that the manifold ...
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Stability condition for AdS background (when gravity coupled to matter fields)

In finding the stability condition for AdS background (when gravity coupled to matter fields), why the conserved energy should be positive?
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Is general covariance a symmetry?

Is general covariance a symmetry? If it is ,what is its symmetry group and corresponding generator?
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Wald problem 4 of chapter 4

I'm trying to derive equation 4.4.51 in Wald's GR book (the second order correction in $\gamma$ term for the Ricci tensor): where $g=\eta+\gamma$. So ...
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Rigid rectangle in Schwarzschild

Say I build a perfect rectangle. Side lengths $l_1$ and $l_2$ and perfect right angles. I am on earth and the metric is given by the Schwarzschild metric. Setting $dt=0$ leads to the spatial ...
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Geodesic distance in de Sitter space

Consider $N$ dimensional de Sitter space embedded in $N+1$ dimensional Minkowski space: $$\eta_{\mu\nu}X^\mu X^\nu=1, \hspace{1cm}\eta_{\mu\nu}=\text{diag}(-1,1,\dots,1)$$ where I set $H=1$ for ...
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Computing the Einstein tensor for a spherically symmetrical metric using the tetrad formalism

I am having some trouble understanding how to use the tetrad formalism. I will start with what I have so far, my question will be after that. I begin with the metric $$ \text{d}s^2 = e^{2a} \text{ ...
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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 ...
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Gravitational redshift of temperature and electrostatic potential

Consider a charged black hole in four-dimensional Minkowski spacetime, with charge $Q$, mass $M>Q$: $ds^2=-f(r)dt^2+\frac{1}{f(r)}dr^2+r^2d\Omega_2^2$, with $f(r)=1-\frac{2M}{r}+\frac{Q^2}{r^2}$. ...
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Is the new Hawking black hole all about photon launch angles?

The new Jan 2014 Hawking paper (arXiv:1401.5761v1) asserts on page 3: The absence of event horizons means that there are no black holes - in the sense of regimes from which light can't escape to ...
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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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Homeomorphism between the space of all Ashtekar connections and spacetime?

Excerpt from an essay of mine: Let $\Psi(\varsigma)$ be the wavefunction in the loop representation, where $\varsigma:[0,1]\to\mathcal{M}$, where $\mathcal{M}$ is spacetime. Then, let ...
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Trapped Surfaces. Any good articles?

I'm currently writing a dissertation on trapped surfaces as minimal surfaces. I have exhausted all of the resources I have, and the internet is pretty limited (in that it is fairly repetitive on just ...
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On the Geroch's argument

During the study of Geroch's argument to prove positive mass theorem, I faced a problem explained below: Suppose $(M,g_{\mu \nu})$ is a four dimensional Lorentzian Manifold and $\Sigma$ is a ...
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352 views

Gauss-Bonnet term in Physics

Given a 4-dimensional compact manifold (torsion free), the Euler characteristic is defined as: $$E_4 ~=~ \int \epsilon_{abcd}R^{ab} \wedge R^{cd}$$ with $R^{ab}$ is the curvature 2-form. Perturb the ...
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Is the equivalence principle in General Relativity an approximation?

I read in web that Einstein used the principle of equivalence to explain General Relativity but we know the gravitation is approximately equal in all of rested frame in gravitional field. In ...
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Schwarzschild metric in a different coordinate system

In PADMANABHAN, Gravitation (Foundations and Frontiers), Cambridge, p $304$, exercice $7.6$, an example of the Schwarzschild metric in a different coordinate system is given : $$\mbox{d}s^2= ...
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Dirac equation in curved space-time with Torsion

I am looking for pedagogical references in which Dirac equation in space-time with curvature and torsion were discussed.
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Curvature and spacetime

Suppose that it is given that the Riemann curvature tensor in a special kind of spacetime of dimension $d\geq2$ can be written as $$R_{abcd}=k(x^a)(g_{ac}g_{bd}-g_{ad}g_{bc})$$ where $x^a$ is a ...
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Is it mathematically possible or topologically allowable for cutouts, or cavities, to exist in a 3-manifold?

A few weeks back, I posted a related question, Could metric expansion create holes, or cavities in the fabric of spacetime?, asking if metric stretching could create cutouts in the spacetime manifold. ...
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Gravitational effects and metric spaces

Could somebody please explain something regarding the Nordstrom metric? In particular, I am referring to the last part of question 3 on this sheet -- about the freely falling massive bodies. My ...
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are pinch-off bubbles valid solutions to general relativity?

are bubbles of spacetime pinching-off allowed solutions to general relativity? With "pinch-off bubble" i really mean a finite 3D volume of space whose 2D boundary decreases until it reaches zero and ...
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How can things at the event horizon slow down and appear to stop to a remote observer?

So they say the remote observer will never see anything fallen to the black hole, because any object will slow down as it gets closer to the event horizon and eventually stop to stay there forever. Am ...
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Variation of Gibbons-Hawking-York term. General boundary condition and total derivatives

It is actually a comment and question to the answer of Robert McNees in the following post: Explicit Variation of Gibbons-Hawking-York Boundary Term In deriving the variation of the extrinsic ...
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Non-local gravitational energy tensor

The well-known derivation of the Landau-Lifshitz gravitational energy pseudotensor, relies on several requirements: 1) that it be constructed entirely from the metric tensor 2) that it be index ...
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How does one show that asymptotically $AdS_3$ spacetimes are locally $AdS_3$?

Time and again I keep reading that any asymptotic $AdS_3$ spacetime is locally isomorphic to $AdS_3$. I tried to find proof of this by analyzing the Riemann tensor $R_{\rho\sigma\mu\nu} $ in Ricci ...
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Precession of Mercury (Python simulation)

I was trying to simulate the precession of Mercury based on the perturbed solution, and my questions about its implementation in python can be seen here: ...
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Maximum Power transmitted using General Relativity waves - cf Schwinger limit

In Electromagnetism, QED says that the linearity of Maxwell's equations comes to an end when field strengths approach the Schwinger limit. Its about 10^18 V/m. What is the corresponding formula for ...
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Schwarzschild metric circular orbits and kepler's 3rd law

I have been looking at the Schwarzschild metric presented to me as the following within lectures: ...
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81 views

What's the physical meaning of gravitational shock wave?

In this paper link.aps.org/doi/10.1103/PhysRevD.50.3666 the authors discuss the gravitational shock wave metric produced by massless particle: $ds^2=-du(dv+4p\,\text{ln}(\rho^2)\delta(u)du)+dx^2+dy^2$ ...
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Covariant versus “ordinary” divergence theorem

Let $M$ be an oriented $m$-dimensional manifold with boundary. As stated in Harvey Reall's general relativity notes (here) or Sean Carroll's book, the "covariant" divergence theorem (i.e. with ...
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Is Energy attracted to Energy?

Newton taught us that bodies with mass attract each other according to the universal law of gravitation (mass-mass attraction) and Einstein taught us that mass and energy are equivalent though his ...
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Is time depending on the observer in string theory?

I heard that in the theory of relativity the time of an action is depending on the observer. But in string theory, is the time also depending on the observer? Are strings acting according to the ...