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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Gauss-Weingarten equation

In E Poisson "A relativist tool kit" p.75 it says that the Gauss-Weingarten relation is: $$e^{\alpha}_{a;\beta}e^{\beta}_{b}=\Gamma^{c}_{ab}e^{\alpha}_{c}-\epsilon K_{ab}n^{\alpha}$$ We have the ...
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Nature of the singularity in the Taub-NUT metric

Consider the Taub-NUT metric $$ds^2=-V(dt+2N(1-\cos\theta)d\phi)^2+\frac{1}{V}(dr^2)+(r^2+N^2)(d\theta^2+\sin^2\theta{}d\phi^2),$$ where $$V=\frac{(r-r_+)(r-r_-)}{(r^2+N^2)} \qquad r_{\pm}=M\pm \...
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Does the rate of observable change within space-time change as time passes?

Mass seems to be one thing the effects the "relativeness of time". Assuming the big bang, if the universe had mass in one central location and the mass is moving away from a singular point it would ...
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How conclusive is “Gravitational red-shift Gedanken”?

The gedanken goes as you take a particle of mass $m$ at a height $H$. Then let it fall to gain the velocity (approximately)$\sqrt{2gH}$ when it reaches the ground. Convert the particle into a photon ...
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Why Newton's gravitational constant remains unchanged in relativity though gravity is not a force?

I know that Einstein described gravity as a curvature of spacetime. So, It is not a "force" but why Einstein had to accept Newton's gravitational force constant?
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What is basic tensor algebra in teleparallel equivalent of general relativity?

Teleparallel gravity represents a viable alternative to general relativity where gravitation comes from torsion rather that curvature. The theory is based on a new modified connection, and the ...
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40 views

Unknown functions in Schwartzchild Metric

I was reading through MTW and they made a big deal about how we were able to make an astute choice of coordinates to eliminate unknown functions from the most general form of the metric for a ...
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Can redshift occur from relative velocity or just from expanding space

With sound the Doppler effect is caused by the wavelength of the sound being affected by the relative velocity between the observer and emitter, eg. If they are moving toward each other the observed ...
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How does one derive Christodoulou Memory Effect?

There is a non-linear effect associated to the permanent displacement of test masses when a gravitational wave interact with them. This is called the Christodoulou memory effect. How does one obtain ...
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Is the distortion of spacetime caused by frame dragging continuously changing, or fixed?

Consider a very heavy star and let´s take a look at the distorted spacetime accompanying the star. Does the spacetime gets increasingly wind up, or is it stationary? If it´s not stationary, then we ...
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Relative motion in particle measurements

I was thinking about measurement of particles at almost-zero energies/temperatures and the movement associated with it. Compared to an observer next to the particle who sees the particle moving at ...
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Non equilibrium black hole radiating away energy and angular momentum, with total energy and angular momentum conserved

The question refers to whether mass (i.e., energy) and angular momentum can be considered to have been carried away by the gravitational radiation in the hole settling down. And whether those entities ...
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When a dumbbell tumbles, is the gravitational wave amplitude dependent on the frequency?

Normally, we think of gravitational waves as being only created by massive objects, which makes using them infeasible. But if the speed of tumbling affects the amplitude of the waves, then we might ...
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How are negative energy orbits around a Black Hole defined?

I have read several times that within the ergosphere or a Kerr Black Hole, it is possible to have particles that have an orbital energy value of less than 0. However, I do not understand the concept ...
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Proper Distance and Coordinate Distance in General Relativity

When I started studying general relativity,I was told that the coordinate distance is not covariant and it does not have any physical meaning.I realized that only the proper length is the physical-...
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Gravity modeled by warping of spacetime or by field field theory?

I've recently read "Fields of Color" by Rodney Brooks who states that there are currently two ways of understanding the phenomenon of gravity. One involves a warping of 4D spacetime a la Einstein, ...
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GR - curve (in)completeness & (in)extendibility

Seeking clarification of the distinction between completeness of geodesics/extendibility of curves in GR spacetimes? (Confirm: not the geodesic completeness of a spacetime but the completeness of an ...
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Help needed to understand Kerr coordinate transformation

The (uncharged) Kerr metric for a black hole of mass $M$ and angular momentum $Ma$ takes the form $$ds^{2} = \Sigma\Big(\frac{dr^{2}}{\Delta} + d\theta^{2}\Big) + (r^{2} + a^{2})\text{sin}^{2}\theta ...
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Simple Question About Repulsive Potential Field Time Dilation

A space-time with a point mass gravitational potential given by $\Phi(r)$ has a metric described by, $$ds^2=-\left(1+\cfrac{2 \cdot \Phi(r)}{c^2} \right) \cdot c^2 \cdot dt^2+\left(1-\cfrac{2 \cdot \...
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What is a zero temperature horizon?

While reading the paper "Disorder horizons: Holography of randomly disordered fixed points" by Hartnoll and Santos, I came across this: We are interested in solutions with a zero temperature ...
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What is the explicit form of $\tau^{\alpha\beta}$ in the linearized Einstein field equations $\Box h^{\alpha\beta}=-16\pi\tau^{\alpha\beta}$?

If we let $h^{\alpha\beta}=\eta^{\alpha\beta}-g^{\alpha\beta}\sqrt{|det(g)|}$ then, according to wikipedia, the Einstein Field Equations become $$\Box h^{\alpha\beta}=-16\pi\tau^{\alpha\beta},$$ where ...
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Gibbons-Hawking-York boundary term expanded at second order in the fluctuation

Does anyone know a general form for the Gibbons-Hawking-York boundary term expanded at quadratic order in the fluctuation of the metric? Assume to define the fluctuation of the metric $g_{\mu \nu}$ ...
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Can a lightlike singularity have nonzero mass?

The effective mass of the Schwarzschild solution is valid at $r=0$. For $m>0$, we have a spacelike singularity, while for $m<0$ we have a timelike singularity. Suppose, instead of a spacetime ...
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Equation of state for a radiation fluid

Can anyone give me (point me to a reference of) a derivation of the equation of state for a radiation fluid: pressure = energy/3 Much thanks.
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Gravity as a gauge theory - Cartan-Killing form?

First, let me state the form of Lagrangian for YM and GR \begin{align} L_{YM} = \alpha \textrm{tr}(F^2), \qquad L_{GR} = \beta R \end{align} I heard, YM is a gauge theory but GR isn't a really gauge ...
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Binary black hole system, near-field geodesics and post-newtonian formalism

I am interested in simulating the following system: Particle trajectory near one black hole (around 6-10 Schwarzschild radius) in the presence of another black hole (more than 50 Schwarzschild radius ...
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112 views

Did the LIGO measure gravitomagnetic waves as well?

I think of gravitomagnetism as as the "magnetic" portion of gravity, with gravity being the "electric" portion. Since gravity ("electric") seems to affect space (which the LIGO could detect) what ...
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What is the current status of Penrose Conformal Cyclic Cosmology?

A brief summary from wikipedia Penrose's basic construction is to connect a countable sequence of open Friedmann–Lemaître–Robertson–Walker metric (FLRW) spacetimes, each representing a big ...
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Photon Gas Stress-Energy Tensor

In standard texts it is typically discussed how one can obtain the stress energy tensor of a perfect fluid, in both coordinate-dependent and coordinate independent forms: \begin{equation} \mathbf{T}=(\...
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64 views

Which formula was used to get Gravitational Waves animation?

I would like to make animation like this by myself It is from wikipedia article "Gravitational wave". But if I use formula from wikipedia article "Gravitational wave" subsection "7.2.2 Wave ...
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Space/time elasticity and state changing

What happens to a particular section of space/time that has been bent due to a large gravitational force that has passed it by? Does it "snap back" to it's original state. Is it permanently bent? Is ...
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Numerical simulation of strong field gravitational vacuum solutions colliding

I am interested in the current state of knowledge of strong field General Relativity learned from numerical investigations of gravitational wave packets colliding with each other or black holes. If ...
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Why is it said that the cosmic censorship hypothesis depends on the future evolution of the spacetime?

I am reading a bit about the cosmic censorship hypothesis and I came across the following statement: Cosmic censorship is precisely a statement on the global future evolution of a spacetime. My ...
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How much time distortion was caused by GW150914?

I understand (at least I think I understand) that LIGO used distortion of space to detect GW150914 (one arm grew longer, the other arm grew shorter, causing interference in the returning laser-pulse ...
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How do gravitational waves and black holes interact?

Following the first detection of gravitational waves yesterday (11 Feb. 2016) by LIGO, I have a couple of questions about how gravitational waves and black holes interact. Assume that there is a ...
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Bondi mass aspect

I'm looking for a good reference that defines the Bondi mass aspect and his relations to Bondi and ADM mass. Googling a bit I've not founded any satisfactory exposition of the subject. A short ...
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Is it accurate to say that nothing can travel faster than $c$ in a GR context, where more space can be created?

Years ago, my brother and I had an argument where I was trying to convince him that nothing could travel faster than the speed of light. I was pursuing this in the context of Special Relativity. My ...
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Can we always effectively describe a timelike worldline (non-geodesic) in one spacetime as a geodesic in some other spacetime?

Can we always effectively describe a timelike worldline (non-geodesic) in one spacetime as a geodesic in some other spacetime with a different metric? Is this implied by the equivalence principle ...
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What are the implications of today's direct detection of gravitational waves?

Here is the announcement from today's Physical Review Letters by Abbott et al.:"On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory ...
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event horizon vs apparent horizon ramifications

If the event horizon doesn’t exist in the 2-dimension or 3-dimension time-space - and it doesn’t exist if it can’t be measured or observed - then an apparent horizon would be necessary to reconstruct ...
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Identity $ \epsilon_{abcd} R^{cd}_{\phantom{cd}mn} = \epsilon_{mncd} R^{cd}_{\phantom{cd}ab}$ in vacuum

starting from \begin{align} \epsilon_{\rho\lambda\xi \kappa} R^{\xi \kappa}_{\phantom{ab} \sigma\tau} + \epsilon_{\rho\sigma \xi \kappa} R^{\xi \kappa}_{\phantom{ab} \tau \lambda} + \epsilon_{\rho \...
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Two black holes prepared from different initial states

I have asked a similar question, I would like to reformulate it in more details. Here is a thought experiment: Assuming we can create black holes by squeezing photons, we can then prepare two ...
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162 views

When is the event horizon a Killing horizon?

I know the definition of both (event horizon is closure of causal past of future null infinity whilst Killing horizon is a null surface where some Killing vector becomes null e.g. the surface where it ...
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General relativity degrees of freedom — simplified version?

I'm afraid my question may be too general, but I would like to ask how I could find out the degrees of freedom in a given tensor. I have had this question since I started studying GR. At first, I ...
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Easy unit conversion in Kerr metric

I would like to use Kerr metric in Boyer-Lindquist coordinates in geometrized units with mass of the black hole normalized to $M=1$. I am embarrassed to admit, but I can't seem to figure out how to ...
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Simple tetrad exercises

I am reading Andrew Hamilton's really nice notes on Tetrad formalism of general relativity, and I am having trouble finding assignments/exercises on tetrad formalism. Would anyone know a good resource ...
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Could we have blue/violet shifting?

As the universe expands, it stretches light into longer wavelengths, resulting in what we know as red shifting. But some say that there is a chance in which the universe will stop expanding and then ...
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Breakdown of correspondence principle: null dust case

In both quantum and general relativity theories we are used to provide results in the "limited" conditions to demonstrate a correspondence between new and old formalism. For instance deflection of ...
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Guesses from a Rindler observer

Suppose an observer travels through Minkowski space $M=\mathbb{R}^4=\left\{x_0,x_1,x_2,x_3\right\}$ on a uniformly accelerated path: \begin{equation} \begin{cases} x_0= R \sinh(\frac{\tau}{R}) \\ x_1= ...
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Spherically Symmetric Metric in Nordstrom gravity

Nordstrom's theory of gravity postulates that the metric is of the form $g_{\mu \nu} = \phi ^2 (x) \eta_{\mu \nu}.$ The field equations, in vacuum are of the form $R=0$, where $R$ is the Ricci ...