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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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 space....
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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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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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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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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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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 ...
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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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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 preudo-...
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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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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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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 ...
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364 views

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{ d}...
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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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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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equation of motion for the scalar field via variational principle in general relativity

I would like to find the equation of motion for the scalar field $\phi$ by varying the following action in General Relativity. Special Relativity: $$ S = -\tfrac{1}{2}\int d^4\xi\, \eta^{ab} \...
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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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Some questions about spacetime topology, causality structures and other GR businesses

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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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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Spaans, “On Quantum Contributions to Black Hole Growth”

This paper was posted to arxiv a couple of weeks ago: http://arxiv.org/abs/1309.1067 From the abstract: The effects of Wheeler's quantum foam on black hole growth are explored from an ...
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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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Showing that the Ricci scalar equals a product of commutators

I have to compute the square of the Dirac operator, $D=\gamma^a e^\mu_a D_\mu$ , in curved space time ($D_\mu\Psi=\partial_\mu \Psi + A_\mu ^{ab}\Sigma_{ab}$ is the covariant derivative of the spinor ...
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Alternate geodesic completions of a Schwarzschild black hole

The Kruskal-Szekeres solution extends the exterior Schwarzschild solution maximally, so that every geodesic not contacting a curvature singularity can be extended arbitrarily far in either direction. ...
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Derivation of the Gauss-Codazzi equation

I'm interested in the derivation of the Gauss equation (Gauss-Codazzi). Usually we consider the definition of the Riemann tensor on the hypersurface. $$^{(n-1)}R_{abc}^{~~~~~~~d}~w_d=[D_a,D_b]w_c$$ ...
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Does the relative speed of time mean there is less energy where time is slower?

Time runs relatively slower near a planet than in outer space. Does this mean that there is less energy near the planet? Is there a relationship between energy and the speed of time? If so, this ...
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Can we dispense with the Manifold in General Relativity?

I am studying Quantum Gravity by Rovelli. In chapter 2, the author describes the path that Einstein followed to arrive to General Relativity (GR). At the end of the discussion of the hole argument, ...
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Postulates of general relativity

Special relativity derives from two postulates: Invariance of $c$ Principle of relativity The same axiomatic procedure is possible for quantum mechanics. Now, does exist a set of axioms for general ...
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Why is Newtonian cosmology correct for curved space?

The Newtonian model of an expanding Universe gives Friedmann's equation exactly for non-zero spatial curvature $k$ (see http://hyperphysics.phy-astr.gsu.edu/hbase/astro/expuni.html). Instead of using ...
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256 views

Can a gravitational wave produce oscillating time dilation?

I was reading about gravitational waves and about laser based detectors. I also read this. As mentioned in the answer, when ever there is a deformation in spacetime, doesn't it also create a minute ...
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Energy Conversion from Mass to Gravitational Wave

How is mass converted to gravitational wave energy by inspiralling binary black holes? Is the gravitational wave energy coming purely from the kinetic energy/gravitational potential of the two black ...
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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 ...
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Contribution to the emblackening factor from massive gravitons

I have been studying the effects of massive gravitons on the emblackening factor $f(r)$; i.e., given a Reissner-Nordstrom AdS geometry $$ds^2=L^2 \left(\frac{dr^2}{f(r)r^2}+\frac{-f(r)dt^2+dx^2+dy^2}{...
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Calculate 3-volume in General Relativity

If I want to calculate the number of boxes that have proper width, length and height of 1 that I can fit into some region of spacetime (assuming that for the first instant for which I'm trying to ...
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Expansion in flat spacetime

I have been studying Raychaudhuri equation and focusing theorem related to it. Focusing theorem says that if the strong energy condition is satisfied and rotation tensor vanishes $\omega_{ab}$=0 then ...
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Why does combining background independence and diffeomorphism invariance force you to conclude that spacetime must be quantized?

I was recently watching a fermilab video on loop quantum gravity and at about 4:20 it is stated that, when combined, background independence and diffeomorphism invariance force you to conclude that ...
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If two black holes about to collide head on, will there be interference pattern in the space in between?

Imagine massive object such as 2 non spinning blackholes accelerate towards each other, just before they collides I wonder what would the region of space in between them would look like? Will it be ...
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Understanding Verlinde: How to get from emergent gravity to MOND

Verlinde ( https://arxiv.org/abs/1611.02269 ) tries to deduce MOND from emergent gravity. Can you help? Emergent or entropic gravity goes back to Jacobson. He starts with the entropy-area connection $...
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Relativistic rotation

Consider the following two scenarios: a) A particle is rotating in the $x-y$ plane about some point fixed in lab frame at a radius $a$ with relativistic angular speed $\omega$. Do not include the ...
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Hamiltonian in gravity with $\Lambda =0$ and using it to generate time translations

Time translation is generated by Hamiltonian. In gravity, the bulk Hamiltonian for closed $d$ hypersurfaces (obtained by ADM decomposition of $d+1$ spacetimes) is 0. This is basically a constraint of ...
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Are the spacelike foliations of a non-static spacetime topologically equivalent?

Assuming a stationary, globally hyperbolic spacetime, I can imagine that all spacelike foliations are topologically equivalent though not all will be identical since the spacetime is not static. Is ...
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Is there an equivalent of Kaluza-Klein for fermionic dimensions?

Taking GR in $D$ dimensions, one can use the process of compactification to turn this into GR in $D-1$ dimensions coupled to a Yang-Mills field. i.e. you start with spin-2 fields and you and up with ...
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Doubt regarding particle dynamics and hydrodynamics in Schwarzschild geometry

The effective potential for particle orbits in the equatorial plane of a Schwarzschild black hole in units $G=M=c=1$ is given by $$V_{\textrm{eff}}=\sqrt{\left(1-\frac{2}{r}\right)\left(1+\frac{l^2}{r^...
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Semi-classical Wheeler DeWitt equation

I am currently working with the Wheeler Dewitt equation and I was wondering if the following "semi-classical" limit makes sense or if something similar already exists in the literature as I would like ...
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Supersymmetry in de Sitter space

Is it possible to construct SUSY theories in de Sitter space? I know statement: dS superalgebras cannot be constructed unless one constructs actions with matter coupled with the wrong signs for ...
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Does this Boltzmann-factor-included metric relate to some known physics phenomena?

When I tried to map the motion of a constant-speed particle with speed $v$ and central force magnitude $k(r)$ to a space-time metric, it turns out the metric is in the form $$d\lambda^2=-\alpha^2 dt^...
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Coordinate or world line? Understanding a simple example problem

I'm trying to follow a simple example from Misner's Gravitation (p. 181). Misner takes the action integral $$I = \frac{1}{2}m\int\left(\eta_{\mu\nu}+h_{\mu\nu}\right)\dot{z}^\mu\dot{z}^\nu\,d\tau,$$ ...
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In General Relativity, can I represent a Tetrad/Frame field in terms of ladder operators?

I've been interested in expressing the metric tensor $g$ in terms of it's harmonic expansions. In particular I'm interested in writing the tetrad/frame-fields in terms of such expansions. For ...
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Initial value problem on $\mathcal{I}^-$ for Maxwell fields

In the paper "Symplectic Geometry of Radiative Modes and Conserved Quantities at Null Infinity" by Ashtekar and Streubel the authors state the following: Fix, as in § 2(a), a conformal completion $(...
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Spin Foam Introductory Texts

What are some good introductory texts on spin foams / LQG for someone specialized in SUSY / string models? I’m somewhat familiar with some of the literature (Topological Amodel and crystal melting / ...
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Addition of velocities in General Relativity

How does one add velocities in general relativity? If I have a particle with a given four-velocity $u_\alpha$ and a metric $g_{\alpha \beta}$ (for example, a Keplerian orbit around a Schwarzschild BH,...

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