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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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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34 views

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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68 views

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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18 views

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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42 views

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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25 views

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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37 views

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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32 views

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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108 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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50 views

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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45 views

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} ...
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49 views

About the non-locality of gravitational energy 2

Gravitational energy is non-local which is essentially because of the equivalence principle. The equivalence principle says that you can always transform your frame so that you feel like in a ...
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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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29 views

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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23 views

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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35 views

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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89 views

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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58 views

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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22 views

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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64 views

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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26 views

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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111 views

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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24 views

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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33 views

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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76 views

A possible proof that time traveling to the past with the aid of a wormhole is impossible?

Suppose a wormhole connects two part of the place where I live. I find myself in a spaceship attached to one side of the hole, and my wife on the other side, so we can see and talk to each other. Now ...
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46 views

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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51 views

Is metric $g$ a representation of Lorentz group? What decides it's transformation properties?

I am confused what representation of Lorentz group does a metric transform under? How does it's transformation properties are decided?
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131 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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44 views

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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31 views

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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44 views

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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54 views

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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36 views

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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30 views

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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46 views

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 ...
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26 views

String spreading?

What is 'string spreading' (in the context of string theory)? Does it have implications for the observability of post-classical effective field theory of gravity terms near macroscopic black hole ...
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49 views

Questions arising from the presentation of “Schild's ladder” in “Gravitation” (Misner, Thorne, Wheeler)

MTW, p. 248, presents a description of "Schild's ladder" construction which I quote here extensively enough for referencing some subsequent questions. A. Transport any sufficiently short stretch ...
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47 views

Bending of light in a gravitational field & the principle of equivalence

I have a few conceptual issues following a standard thought experiment to argue why light bends in a gravitational field and I'm hoping I can clear them up here. Consider an observer in a lift in ...
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32 views

Dark Energy Density Paramater For Unlimited Expansion

Suppose that the universe is dominated by matter and dark energy. Let $\Omega_m$ and $\Omega_\Lambda$ denote the respective relative density parameters. Given $\Omega_m$, what does $\Omega_\Lambda$ ...
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27 views

Are only measurements registered as events?

When we measure an electron or some other system behaving quantum mechanically, we observe something. Now, this can be called as an event in relativity terms meaning if we live in 1-D spacetime, only ...
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38 views

Gibbons-Hawking Variation

I know there already exist some questions about this and some very good answers. However, I am still having trouble understanding one part of the calculation. The GHY term is given by ...
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10 views

DGP model, minus one dimension

Is there a name for a theory like the DGP model, but with one fewer dimension? That is, a theory whose action consists of the 4D Einstein Hilbert action at long distances, and the 3D one at small ...
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32 views

Expression for the energy in the limit case of weak gravitational field

I'm trying to solve the following problem of General Relativity. Consider a particle of mass $m$ which moves following a geodesic in a space-time with metric $$ ds^2 = - ...
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82 views

Gravity's force on space

Here is a quote from Brian Greene, The Fabric of the Cosmos: Space, Time, and the Texture of Reality, p. 273: “The early universe provided an arena in which gravity exerted its repulsive side with ...
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75 views

Does rest mass increase in the FRW metric?

The flat FRW metric can be written in conformal co-ordinates: $$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$ where $\eta$ is conformal time. Let us assume that $a(\eta_0)=1$ when $\eta_0$ is the present ...
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47 views

Definition of Energy in Friedmann equations?

The first Friedmann equation for a flat Universe is given by: $$\bigg(\frac{\dot{a}(t)}{a(t)}\bigg)^2 = \frac{8 \pi G}{3} \rho(t)$$ The energy density $\rho(t)$ is given by: $$\rho(t) \propto ...
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34 views

How to derive the relation satisfied by “gravitational magnetic field” from an equation of the Weyl tensor?

Let us call the spacetime $M$ with a metric $g_{ab}$. There is a unit spacelike vector field $\eta^a$ orthogonal to a hypersurface. So that we can define the so-called gravitational electric and ...
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77 views

Why is special relativity still in use, if general relativity is more broad?

I always thought special relativity is only there because it is the building block for "The General theory of Relativity", until recently I encountered a text from my course book given below. A ...
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35 views

Local Translation of frame field- Geometric Picture

In order to phrase my question I review my geometrical picture of the first order formulation of gravity: Given some d-dimensional manifold $\mathcal{M}$ one constructs the Frame bundle $FM$, a ...
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33 views

Solving the Stress-energy-momentum tensor with metric

Let's say I want to find an expression for $T_{00}$ in Einstein field equations given a particular metric. I need to find first $g_{00}$, which is not complicated to find, and $R_{00}$ which is ...