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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289 views

Gravitation and the QFT vacuum

I'm asking this to get yet another lessson in the inability of QFT and GR to cohabit. Many people believe GR must yield to quantization. The question here is as to why the activity of the vacuum ...
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28 views

Explanation of galaxy rotation curves by space-time drag

I expect, that known effect of rotating body (made of galaxy stellar mass) it too small to explain galaxy rotation curves. By how small is it comparing to required value? What if introduce ...
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126 views

What is the mass and density distribution of a Schwarzchild black hole in the viewpoint of distant observer?

According to Schwarzschild metric the density element $$ \frac{\mathrm dm}{\mathrm dV} $$ becomes infinite on the event horizon if there is mass $$ \mathrm dm > 0 $$very near at the outside of ...
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26 views

Killing Horizon for a space-time metric

How many Killing Horizon (KH) are possible for a particular S.T. metric. Because there is a surface gravity associated to each KH, which is constant over KH surface. Do a Black Hole have many surface ...
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57 views

On the definition of Lagrangian

I have a question about "the definition of Lagrangian" in spacetime manifold. In general relativity, the energy-stress tensor and the vacuum energy stress tensor can be written as below: $$T_{\nu\mu}=...
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9 views

How to calculate the lensing amplification of the weak field images in schwartzchild metric?

In Strong field limit of black hole gravitational lensing, Bozza et al state (without proof) that the amplification of each weak field image is given by $$ \mu_{wfi}=\frac{1}{\beta}\sqrt{\frac{2\,D_{...
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27 views

Removing temperature from black hole

Suppose I take the metric of a three dimensional AdS-Schwarzschild black brane (Note not actually a black hole!): $ds^2 = \frac{L^2 dr^2}{r^2 W} + \frac{r^2}{L^2} \left[ - W dt^2 + dz^2 + dx^2 \right]...
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56 views

Hughston, Todd General Relativity Problem 5.2

Hey everyone I am trying to solve the following problem in Hughston Tod: A manifold is endowed with a connection such that $$(\nabla_a\nabla_b-\nabla_b\nabla_a)V_c=T^d_{ab}\nabla_d V_c $$ For any ...
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30 views

How do I use the value I get from the gravitational time dilation formula to calculate dilated time?

I am trying to calculate gravitational time dilation with the following formula: $\exp\left(\dfrac{1}{c^2}\cdot-\dfrac{GM}{h}\right)$, where $-\dfrac{GM}{h}$ is the integral of the g function, and $\...
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103 views

Intuition behind deriving the FRW metric

I am studying the FRW metric and am looking at a motivation for it here. The motivation seems to use four spatial dimensions. Why do we need the fourth spatial dimension in this? This doesn't seem ...
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30 views

Can orbiting a black hole 99.99% speed of light make other object with relatively fast clock travel faster than light, relative to me?

If i orbit a black hole, 99.9% speed of light, time for me is moving slowly, relative to me, planet earth is aging fast, and i have traveled 10 years into the future(relatively) in 1 second, suppose ...
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26 views

How small can a sample size be of space to detect space-time curvature?

What is the minimal sample size of space necessary to detect space-time curvature?
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53 views

Does gravitational radiation have a formalism similar to Wheeler-Feynman electrodynamics?

Binary systems radiate energy away in gravitational waves as the orbits of the two masses spiral in towards each other. My understanding of gravity is that we think of it as a mediator of particle-...
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52 views

Second derivative of the stress-energy tensor

Which physical meaning can have if the second derivative of stress-energy tensor is zero? In General Relativity or elsewhere.
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31 views

Behavior of an object in a region of uniform spacetime curvature

Let's say there is some spherical region of space. In this region, there is a large curvature of spacetime. This curvature is completely uniform throughout the region. I decide to stick some object ...
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47 views

What is the connection between the coordinate transformation properties and graphical representation of covariant and contravariant components?

So right now I am studying General Relativity (in particular tensor analysis), and I have a question regarding covariant and contravariant components of a vector. I was taught how to transform ...
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36 views

What expression of Ricci tensor should we choose in order to obatin a correct field equations?

I have doubt regarding the choice of the Ricci tensor $R_{ij}$. I have seen many books and papers use the expression $R_{ij}=\Gamma^i_{jp,i}-\Gamma^i_{ji,p}+\Gamma^i_{in}\Gamma^n_{jp}-\Gamma^i_{pn}\...
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36 views

Do time and spatial derivative under a 3+1 decomposition commute?

After a certain 3+1 decomposition of the space-time, the derivative of time part and spatial part separate. Let's denote them by $d_t$ and $\partial_\mu$. Here the spatial derivative is covariant but ...
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36 views

Variation with respect to the metric and other tensors

When varying an action with respect to tensors and the metric, I'm afraid I get confused as how to one organizes the Lagrangian and then performs the variation. Take for example, the following example ...
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54 views

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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37 views

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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30 views

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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54 views

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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55 views

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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41 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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19 views

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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40 views

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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17 views

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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28 views

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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27 views

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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17 views

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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23 views

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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52 views

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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56 views

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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36 views

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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36 views

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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19 views

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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36 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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72 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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43 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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36 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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44 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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33 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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114 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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97 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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53 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} \mathbf{T}=(\...
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65 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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32 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 ...