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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530 views

General relativity vs graviton discovery

Will the discovery of the graviton lead to the redundancy of general relativity even though it has been so well established. If not, will it mean that gravity will have two separate theories that ...
2
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2answers
57 views

Projection of a tensor

Consider the following tensor (abstract index notation, e.g. Wald's) $B_{ab}$ and timelike vector field $X^{a}$ such that $X^aX_a=-1$ and \begin{equation} B_{ab}=\nabla_bX_a \end{equation} Then one ...
2
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0answers
62 views

(1+1)-General Relativity

Goodevening everyone, my question is: What is the interest of studying the (1+1)dimension General Relativity? Can you explain please? Thank's in advance!
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2answers
69 views

General relativity applications other than gravity

Do the Einstein field equations successfully predict/describe physical processes other than gravitational ones?
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0answers
25 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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0answers
23 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?
2
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1answer
58 views

Metric with Harmonic Coefficient and Stress-Energy Tensor in General Relativity

I have two question: Is there any possible implies or interest to use in general relativity a metric whose coefficients are harmonic functions? What is the meaning (physical) if the stress-energy ...
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0answers
38 views

Lagrangian density

I really wonder : Why do we take Lagrangian density as zero for the Stokes theorem in Minkowski-space at infinity? Is there a proof of this situation?
4
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2answers
110 views

What does string theory predict for the singularity inside a black hole?

The usual explanation for what's going on inside a black hole goes something like "General Relativity predicts a singularity with infinite curvature, but when matters gets so tightly compressed we ...
0
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0answers
46 views

Einstein's quote relating to absoulute frame [on hold]

There were two main objections to the concept of Absolute Space,as written in Relativity SPECIAL, GENERAL, AND COSMOLOGICAL by Wolfgang Rindler. They are (i) Absolute space cannot be ...
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1answer
49 views

Black hole gravity at bottom (deepest end) [on hold]

If black holes are hole in space and time then at bottom or below bottom there is no more gravity of black hole. As any hole has an end (Deepest end). Is this true ? ******** EDIT *********** http:/...
3
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1answer
81 views

Exotic differentiable structures in physics

When reading a bit on exotic spheres and exotic $\mathbb{R}^4$'s, I came across some papers of Carl H. Brans and Torsten Asselmeyer-Maluga: "Exotic differentiable structures and general relativity" (...
10
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3answers
2k views

Will a giant ball of protons form a black hole?

Suppose you have enough energy and resources to put together (in a momentarily static configuration in which they are all at rest at the same time) as many protons as you want to form a "proton star". ...
5
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2answers
79 views

What is “a general covariant formulation of newtonian mechanics”?

I am a little confused: I read that there are general covariant formulations of Newtonian mechanics (e.g. here). I always thought: 1) A theory is covariant with respect to a group of transformations ...
0
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0answers
49 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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0answers
57 views

Conformal invariance of Maxwell equation in presence of external current

It is known that pure electrodynamics in curved space-time is invariant under Weyl transformations $$ \tag{1} g_{\mu\nu} \to \Omega(x)g_{\mu\nu}, \quad F_{\mu \nu} \to \Omega^{-1}(x)F_{\mu\nu}. $$ ...
2
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1answer
51 views

Age of universe from Hubble's constant

Assume the Robertson-Walker metric: $$g = -d\tau^2 + a^2(\tau)\gamma$$ where $\gamma$ is the flat, spherical or hyperbolic spatial metric and $a$ is the scale factor. Wald seems to calculate the age ...
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0answers
61 views

Relativity - Twin Paradox and Absolute Frame of Reference - Why Not? [closed]

Absolute Reference Frame is a very discussed topic here and at other forums. For me it seems natural that the Relativity twin paradox should be explain in respect to such frame. The wikipedia article ...
1
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0answers
26 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 ...
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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
117 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 ...
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, ...
1
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0answers
94 views

Deriving the field equations for a dark energy / modified gravity effective field theory

Question I'm trying to derive the modified gravity EFT field equations and, from their 00 component, this Friedmann equation: \begin{equation} H^{2}+H\frac{\dot{\Omega}}{\Omega}=\frac{\kappa \rho_{m}+...
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 ...
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}...
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0answers
47 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.
3
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1answer
104 views

Derivation of Christoffel Symbols

So I am reading a book on relativity & differential geometry and in the text, they gave the Christoffel symbols in terms of the metric and its derivatives, but I wanted to derive it myself. ...
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0answers
43 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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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 ...
1
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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, ...
17
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2answers
2k views

What is black hole spin?

First of, congrats to the people at LIGO. In this article, the BBC notes that the latest LIGO results show that a new black hole was formed with a spin of $0.2$ (dimensionless number). What exactly ...
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1answer
151 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 ...
3
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1answer
90 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 ...
0
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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
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2answers
107 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 ...
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 ...
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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?
2
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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?
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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 ...
1
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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 ...
0
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1answer
53 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
69 views

Uncommon tensor notation $\partial_{(\mu}\xi_{\nu)}$

I came across this expression for the change in a metric under an infinitesimal gauge transformation $\epsilon\xi^\mu$. $$h_{\mu\nu}' = h_{\mu\nu}+2\epsilon\partial_{(\mu}\xi_{\nu)}$$ What does the $...
53
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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 ...