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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665 views

What is the equation for the scale factor of the universe, a(t), for the best fit of data to the $\Lambda CDM$ Model of Cosmology?

Ideally I like a single formula or multiple formulas for different time ranges that would cover the time from the end of inflation through 100+ billion years after the big bang using the $\Lambda CDM$...
1
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0answers
27 views

How to find tetrads corresponding to a given metric?

In General Relativity, sometimes doing calculations with a set of orthonormal tetrads $h^{a}_{\mu}$ where $h^{a}_{\mu}$$h^{b}_{\nu}$$\eta_{ab}=g_{\mu\nu}$ for some metric $g_{\mu\nu}$ is easier ...
-3
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0answers
45 views

How to work out a black hole radius if you know its density

How would you work out the size of the Schwarzschild radius knowing the energy density of a black hole?
2
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1answer
119 views

What is the relation between the metric tensor and the graviton?

In Zee's quantum theory in a nutshell, at the end of chapter I.10, he states that the graviton is of course the particle associated with the field $g_{\mu\nu}$. My understanding of quantum ...
7
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2answers
404 views

Wave packet in curved spacetime

It is known that the classical equation of motion for a scalar field wave packet on a curved spacetime background gives the geodesic trajectory (the e.o.m. is $(\nabla_\mu \nabla^\mu + m^2) \Phi=0$). ...
60
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8answers
5k views

Turbulent spacetime from Einstein equation?

It is well known that the fluid equations (Euler equation, Navier-Stokes, ...), being non-linear, may have highly turbulent solutions. Of course, these solutions are non-analytical. The laminar flow ...
4
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0answers
45 views

Is the Weitzenböck connection the only connection with Torsion but without Curvature?

In teleparallel gravity, the (local) connection coefficients of the Weitzenböck connection are given by $$ \Pi^{\beta}{}_{\mu\nu}= h^{\beta}_{i} \partial_{\nu}h^{i}_{\mu} - \Gamma^{\beta}{}_{\mu\nu}...
3
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3answers
113 views

Why is the photon-sphere around a Kerr Black Hole spherical and not ellipsoid?

Kerr Black Holes have usually (excluding extrema $a=0$, $a=1$) due to their spinning activity an ellipsoidal ergosphere. So why does the photon-sphere does not have an ellipsoidal form? http://...
0
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1answer
62 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 ...
2
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1answer
43 views

Mathematically deriving Hubble's constant

Assuming homogeneity and isotropy, the spacetime metric is of the form $g = -d\tau^2 + a^2(\tau)\gamma$ where $a$ is the scale factor and $\gamma$ is the spatial metric corresponding to a flat, ...
0
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1answer
54 views

Qualitative picture or reference for a Lemaître's Cold Big Bang theory

Warning: please, consider this question to be motivated by historical curiosity or as an exercise in model-building. I believe this cannot be considered non-mainstream physics as it was very much ...
1
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1answer
82 views

How is Riemann tensor related to the curvature in the coordinates?

I came across statements such as "the acceleration observed in a weak gravitational field is mainly due to curvature in the time coordinate. " I want to know how we can explicitly find the curvature ...
0
votes
1answer
118 views

Gravitational Time Dilation vs Acceleration Time Dilation

I might be a little dense to this subject, but I would like to ask a question relating to this one ( Is gravitational time dilation different from other forms of time dilation? ) but asking if this ...
7
votes
2answers
312 views

Non-trivial scalar quantity

Is there any scalar quantity made of only the Christoffel symbols, determinant of a metric and tensors, not derivatives? In other words, can we construct a scalar quantity which cannot be written in ...
2
votes
2answers
153 views

Does negative mass reverse the arrow of time?

General relativity predicts that normal mass (positive mass) results in the curvature of spacetime which in return leads to gravitation. Since space and time are bonded together, any change on the ...
20
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2answers
2k views

Is spacetime flat inside a spherical shell?

In a perfectly symmetrical spherical hollow shell, there is a null net gravitational force according to Newton, since in his theory the force is exactly inversely proportional to the square of the ...
3
votes
2answers
151 views

General expression of the redshift: explanation?

In some papers, authors put the following formula for the cosmological redshift $z$ : $1+z=\frac{\left(g_{\mu\nu}k^{\mu}u^{\nu}\right)_{S}}{\left(g_{\mu\nu}k^{\mu}u^{\nu}\right)_{O}}$ where : $S$ ...
12
votes
1answer
399 views

How long can a particle survive inside of the horizon of a black hole?

By examining the causal structure of a Schwarzschild black hole, one can see that a particle in region II is unable to escape to $r=\infty$. Such diagrams do not show, however, how long a particle ...
-1
votes
0answers
44 views

What is the significance of the so called Planck force? [duplicate]

So, what is the significance of the so called Planck force, and why is it called Planck force, when it has nothing to do with any of the Planck's discoveries? The Maxwell’s wave equation is $\nabla^...
0
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0answers
48 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.
7
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2answers
777 views

Deriving Gauss-Bonnet Gravity (Or just higher order corrections)

I have been working for some time now on deriving the equations of motion (EOM) for the Gauss-Bonnet Gravity, which is given by the action: $$\int d^D x \sqrt{|g|} (R^2-4R_{ab}R^{ab}+R_{abcd}R^{abcd})...
1
vote
1answer
49 views

The form of the metric after a dimension is compactified

Upon the compactifiation of one spatial dimension, it is said (as though an axiom) that the 5 dimensional spacetime metric separates into a 4 dimensional metric, a vector, and a scalar, (4D gravity, ...
3
votes
1answer
218 views

Deriving the Poisson bracket relation of the Ashtekar variables

I'm trying to figure out how to calculate the orthogonality of Ashtekar variables with respect to the ADM hypersurface metric and conjugate momentum. $$\{{A_a}^i(x), {E^b}_j(y)\} = 8 \pi \beta \delta^...
0
votes
1answer
52 views

Speed of light when accelerating

I'm studying special relativity and saw the 2 postulates of Einstein. The most remarkable one for me is the universal speed of light. Einstein postulated that the speed of light in vacuum is the same ...
13
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1answer
2k views

What is the maximum time dilation factor when orbiting a rotating black hole?

Suppose one spaceship is stably orbiting a rotating black hole and another is far away from the black hole. What is the maximum time dilation factor between the two ships? Can it be made arbitrarily ...
3
votes
1answer
91 views

The most general way to write flat space metric [closed]

What is the most general way to write flat space (in d=4 in particular), but still preserving some isometries? In particular I'm interested in the case with 2 isometries, basically by using explicitly ...
3
votes
1answer
69 views

Is there high ring-down frequencies in LIGO's recent discovery?

This question is from Physics overflow: question in physicsoverflow. I am reading LIGO's new discovery of gravitational waves by black hole merger. During the merger, two phases are not hard to ...
3
votes
2answers
110 views

Proving constant curvature

I'm currently on section 5.1 in Wald's book. He is trying to prove that the cosmological principle implies that space has constant curvature. Given a spacelike hypersurface $\Sigma_t$ for some fixed ...
-9
votes
1answer
154 views

Why does Ligo's second detection of gravitational waves and a black hole merger look absolutely nothing like the first? [closed]

Why does Ligo's reported second detection of gravitational waves and a black hole merger look absolutely nothing like the first detection announced in Februaray? Here is the data from the first LIGO ...
2
votes
2answers
2k views

How long did inflation take to happen?

If inflation happened, it ended about 13.7 billion years ago. But how long was inflation going on before that? Was it just a short burst of time so that it's really okay to say that the age of the ...
3
votes
2answers
125 views

What kind of fundamental interaction is gravitation?

Einstein showed that gravitation is not a force but a effect caused by curvature of space time. Then why does theories of quantum gravity treats gravitation as one of fundamental force?
17
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3answers
2k views

Is the speed of sound almost as high as the speed of light in neutron stars?

Have you ever wondered about the elastic properties of neutron stars? Such stars, being immensely dense, in which neutrons are bound together by the strong nuclear force on top of the strong gravity ...
1
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1answer
165 views

Ernst potential from Kaluza-Klein reduction of axisymmetric space-time

Following appendix A of "Ergoregions in Magnetised Black Hole Spacetimes" by G. W. Gibbons, A. H. Mujtaba and C. N. Pope, starting from the Lagrangian $$\mathcal{L} = \hat{R} - \hat{F}_{\mu\nu}\hat{...
2
votes
2answers
2k views

What is the relation between orbital velocity and escape velocity in strongly relativistic situations?

For practical purposes, I'm considering a non-rotating black hole or neutron star, because I find Kerr black holes a little confusing. The ratio between orbital velocity and escape velocity in ...
0
votes
0answers
28 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 ...
3
votes
2answers
499 views

Locally flat coordinate and Locally inertial frame

I am having some doubts on myself regarding the above concepts in General Relativity. First, I want to point out how I understand them so far. A male observer follows a timelike worldline ($\gamma$) ...
-1
votes
2answers
95 views

Is the spacetime for gravity described with gravitons flat?

Gravity has two equivalent descriptions. One is general relativity, the other is the mechanism by the exchange of gravitons. Is in the latter the spacetime flat?
0
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1answer
60 views

Relativity on a universal scale

Imagine there was a clock on a planet the same size as earth, travelling at the same speed through space, and that this planet was at the most distant part of the universe from earth. If we had a ...
2
votes
2answers
256 views

Coordinate Singularity in Metric

Suppose I have some metric $$ds^2=g(t)dt^2+\frac{1}{r}dr^2$$ which has a singularity at $r=0$. However, if I make the coordinate transformation $u=\frac{1}{r}$, then I get: $$ds^2=g(t)dt^2+r^3 du^...
2
votes
3answers
80 views

Can black holes grow via accretion of dark matter particles?

I'm assuming that the answer to the question in the title is a resounding yes. Since Baryonic matter and dark matter interact via gravitational forces. If this is the case how is information not lost ...
0
votes
2answers
54 views

Locally remove a gravitational field

Let $K$ be an inertial frame of reference on $\mathbb{R}^3$ and $g=g(t,x)$ a nonuniform and nonstatic gravitational field. How I can choose a system of reference $\bar K$ such that mechanical effects ...
6
votes
2answers
484 views

Does the current acceleration of universe imply that our universe is open?

Does the current acceleration of universe imply that our universe is open? If the universe is closed, from the Friedmann's equation, the acceleration of universe wouldn't be possible, would it be? (Of ...
2
votes
0answers
41 views

Can we express QFT in R^8 where the spacetime can be embedded in?

A smooth, 4-dimensional manifold can be embedded in $R^8$. Isn't it a natural selection of space for QFT when we try to extend QFT with gravity?
53
votes
8answers
12k views

If the speed of light is constant, why can't it escape a black hole?

When speed is the path traveled in a given time and the path is constant, as it is for $c$, why can't light escape a black hole? It may take a long time to happen but shouldn't there be some light ...
1
vote
1answer
51 views

How to calculate the free energy in curved space?

To study the Hagedorn temperature of string near a black hole, we need to calculate the free energy in curved space. This is can be done calculating a torus path integral, but I want to know if an ...