All Questions
Tagged with black-holes general-relativity
2,491
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Necessity of Singularity in General Relativity
The Schwarzschild solution is the standard example used to describe a black hole, its important points being the event horizon and the central singularity. But this solution is derived by assuming an ...
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How to derive Smarr formula for Kerr Black Hole?
Following is the Smarr formula for Kerr Black Hole
$$M=\frac{\kappa A}{4\pi}+2 \Omega J $$
where $\kappa, \Omega$, $J$ and $A$ are surface gravity, angular velocity, angular momentum and surface area ...
- 59
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What happens if $ a^2 > M^2 $ in Kerr metric?
(Boyer-Lindquist coordinates and $ c = G =1 $ taken)
As I know, line element in Kerr metric $ d s^2 = - \left( 1 - \frac{2Mr}{\rho^2} \right) d t^2 - \frac{4 M a r \sin^2 \theta}{\rho^2} d \phi d t + \...
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Hawking Temperature of the BTZ Black Hole
The metric of the BTZ Black Hole is given by
$$
ds^2 = - N^2 dt^2 + N^{-2} dr^2 +r^2(d\phi + N^\phi dt)^2
$$
with
$$
N^2 = -M+ \frac{r^2}{l^2} + \frac{J^2}{4 r^2}, \ \ \ \ \ \ N^\phi = -\frac{J}{2r}...
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End points of event horizon
I am reading The Nature of Space and Time by S. W. Hawking. In the last paragraph on page 16 he said that:
event horizon may have past end points but don't have any future end points
I understand ...
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3
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Is the size of a black hole singularity smaller than a fundamental particle?
I am wondering about the size of a black hole singularity. We know that a classical black hole is infinitely dense. I am not asking about size of event horizon. I am asking about actual size of the ...
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Does black hole formation contradict the Pauli exclusion principle?
A star's collapse can be halted by the degeneracy pressure of electrons or neutrons due to the Pauli exclusion principle. In extreme relativistic conditions, a star will continue to collapse ...
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Conservation of Komar mass
The definition of Komar mass in GR is associated with one asymptotically flat end. However, a hypersurface may contain more than one end, such as the spacelike Einstein-Rosen bridge in Kruskal ...
CommunityBot
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Are there Schwarzschild solutions to EFE with the Landau-Lifschitz Pseudotensor?
I read that solving the Einstein Field Equations can sometimes lead to the problem of non-conservation of energy and that the Landau-Lifschitz Pseudotensor resolves this problem.
I can't however find ...
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Energy of the gravitational field within a sphere of radius $R$ in the Schwarzschild metric
The Landau-Lifshitz energy-momentum pseudotensor $t^{μν}$ is defined by
$$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}]...
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Memory effects from black hole migration in the early universe
Let's say that there is a black hole at the center of a galaxy. When this galaxy is merging with another galaxy, it moves through space. If I am looking at a black hole now, there is a certain region ...
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David Tong, notes on General Relativity, pg. 25
I was studying GR using David Tong's notes, which I find very compelling and easy to read. The material is explained clearly to a fault, and I would recommend anyone picking up GR to at least skim ...
- 207k
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Does gravity accelerate you towards the geodesic of light between you and the mass?
If there's a planet far away, you will accelerate straight towards it due to gravity. If you place a Schwarzschild black hole right in the middle between you and the planet (the distance between the ...
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Orthogonal complement of null vector [closed]
I am trying to solve excercise 8.5 d) from Straumanns book on general relativity (here V is an n-dimensional Minkowski vector space):
Prove that the orthogonal complement of a null vector is an $(n-1)$...
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Why does angular momentum shorten the Schwarzschild Radius of a black hole?
Angular momentum causes the event horizon of a black hole to recede. At maximum angular momentum, $J=GM^2/c$, the Schwarzschild radius is half of what it would be if the black hole wasn't spinning.
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