All Questions
64
questions
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35
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Energy of the gravitational field within a sphere of radius $R$ in the Schwarzschild metric
The Landau-Lifshitz energy-momentum pseudotensor $t^{μν}$ is defined by
$$16πt^{μν}
= -2G^{μν} - g^{-1} \left[ -g \left( g^{μν}g^{αβ} - g^{μα}g^{νβ} \right) \right]_{,αβ}$$
where $g=\text{det}[g^{μν}]...
- 366
3
votes
2
answers
84
views
How is it that energy of matter yields gravity if the amount of energy in a system is frame dependent while the force caused by gravity is not?
I've been told that the gravitational field arises due to the energy density terms in the stress-energy tensor of matter and therefore that all energy of matter exerts a gravitational field effect, ...
- 531
2
votes
1
answer
71
views
On the existence of Gravitational energy in GR [duplicate]
I was reading this paper that puts forward the argument that Gravitational energy in GR is unnecessary and doesn't exist and that got me wondering if this is a fringe theory or what exactly is the ...
- 117
0
votes
2
answers
48
views
How does the amount of energy bound in the gravitational field of an object relate to the energy of the object?
If I understand correctly, there is energy bound in a gravitational field, although acceleration of the body that causes the field is required to release some of that energy (in the form of ...
- 15
2
votes
1
answer
222
views
Stress-energy-momentum tensor and potential energy
The stress-energy-momentum tensor in General Relativity includes a mass density terms, which is related to energy via $E=mc^2$. How does potential energy figure into this, since potential energy is ...
22
votes
4
answers
3k
views
Does the gravitational field have a gravitational field?
I am currently reading electrodynamics from Feynman. When talking about the energy of the electromagnetic fields, he says that the location of the field energy could be known at least theoretically ...
- 639
2
votes
1
answer
346
views
Right hand side of Einstein field equation
Why can't the RHS of the Einstein field equations take a form like $T_{\mu \nu}$ plus some coefficient multiplied with $g_{\mu \nu} T$?
It should also be covariantly conserved, I suppose? For example, ...
- 41
2
votes
1
answer
118
views
Does the energy-momentum tensor inside Einstein's field equation include gravitational stress-energy?
The Einstein field equations
$$
R_{\mu\nu} - \dfrac{1}{2}Rg_{\mu\nu} = \kappa T_{\mu\nu}
$$
relate the space-time curvature $R_{\mu\nu}$ to the stress-energy $T_{\mu\nu}$ present in the system. I ...
- 391
0
votes
0
answers
118
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A question about de Sitter-invariant general relativity
In the case of standard general relativity, all solutions to the gravitational field equations are spacetimes that reduce locally to Minkowski. Einstein’s equation is written as
$R^{\mu \nu}-\frac{1}{...
- 113
2
votes
1
answer
168
views
Solving for the metric of a spherically symmetric stationary (but not static) energy distribution that only moves in positive $r$ direction
I want to solve for the metric of a spherically symmetric stationary, but not static energy Distribution. Where there is time translation symmetry, but not time reflection symmetry, and the ...
- 143
0
votes
0
answers
32
views
What energy in GR? [duplicate]
What is energy in GR. My professor has mentioned several times that GR introduces a manifold in place of Euclidean space. He goes on to say that on a manifold it is not possible to add vectors anymore ...
- 69
0
votes
0
answers
71
views
Nonlocal Gravitational energy: How to localize nontrivial topology in GR?
Ok, This question has been beaten to death. I just wanted to look at it from a slightly different angle: Einstein, Rosen, and later Wheeler considered the possibility of particles as spacetime ...
- 2,847
1
vote
1
answer
150
views
Doubt about General relativity
Matter and [non-gravitational] energy via the stress tensor can cause spacetime curvature because the stress tensor is algebraically related to the Ricci curvature tensor, according to Einstein's ...
user229112
5
votes
4
answers
2k
views
Does solving Einstein's field equation depend on Newtonian equations?
It seems that Einstein's field equation in a vacuum depends on Newton, to actually be solved.
$$R_{ij}=0$$
where we assume in the weak gravity limit, it reduces to Poisson's equation.
Now, I suspect ...
- 1,324
1
vote
0
answers
112
views
Interpretation of Angular Momentum flux from stress energy tensor in Black hole superradiance
While studying the superradiance of a scalar field in Kerr geometry, we show that the energy and angular momentum of the Kerr black hole are extracted by the superradiant modes. I understand the ...
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