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Results tagged with black-holes
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user 53098
A black hole is a region of spacetime from which nothing can escape. More formally, the future light cone of any observer within the black hole is completely contained in the black hole, and the black hole region is not within the past light cone of any observer that goes to spatial infinity in an infinite amount of time.
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How can black holes be point-like but have a size?
The size of a black hole is defined by the radius of its event horizon, instead of the "size" of the singularity. Plus, a singularity is not a point, but a spacelike hypersurface.
As long as you are …
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Do all the spacelike curve terminate at the spatial infinity $i_0$ in the Penrose Diagram of...
Let's restrict to the radial direction, so the metric can be expressed as
$ds^2=-(1-r_S/r)dt^2+(1-r_S/r)^{-1}dr^2$
with $r_S$ the Schwarzchild radius. Expressed in Kruskal coordinates, the metric is …
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Higher dimensional trapped surface and its condition?
In higher D-dimensional spacetime, a marginally trapped surface is a closed spacelike (D-2)-surface whose outer null normals have zero convergence. It is very like a marginally trapped surface in the …
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A problem with ADM mass in the derivation of 1st law of black hole thermodynamics
The definition of ADM mass is
$$M=\frac{1}{16\pi}\lim_{r\rightarrow\infty}\int \left(\frac{\partial h_{\mu\nu}}{\partial x^\mu}-\frac{\partial h_{\mu\mu}}{\partial x^\nu} \right)N^\nu dA$$
according …
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Calculate the mass of a Schwarzchild black hole with Komar integral
I lost one term, which is the one containing $\nabla^t(\partial_t)^r=g^{tt}\Gamma^r_{tt}=-M/r^2$, so this term is
$$
-\frac{1}{8\pi}\int r^2\sin\theta \nabla^t(\partial_t)^r d\theta d\phi=\frac{M}{8\ …
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Help me calculate the Euclidean action of a gravitating system!
I recently read Gibbons and Hawking's paper Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752. I am interested in repeating their calculations.
It is fairly si …
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3
votes
1
answer
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The Killing vector at the bifurcation surface of a stationary black hole
In the paper Black Hole Entropy is Noether Charge, Wald related the black hole entropy to the Neother charge using the covariant phase space formalism. In proving this relation, Wald noticed that on t …
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answer
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Calculate the mass of a Schwarzchild black hole with Komar integral [closed]
In Wald's GR, Komar integral is Eq. (11.2.9):
$$M=-\frac{1}{8\pi}\int_S\epsilon_{abcd}\nabla^c\xi^d$$
$S$ can be chosen as a 2-sphere, the boundary of a spacelike hypersurface $\Sigma$ such that the …
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