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Results tagged with black-holes
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user 124838
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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2nd order perturbation of a charged rotating body
What is the 2nd order perturbation to the flat Minkowski metric $\eta_{ab}$ caused by a charged, rotating body? In particular, if we take a metric $\eta_{ab} + h_{ab} $, what $h_{ab}$ satisfies the Ei …
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Deriving a Schwarzschild radius using relativistic mass
John Rennie, I think we should clarify that when you go from the second metric to the first, you first perform the transformation $dx^2+dy^2 + dz^2=dr^2 + r^2 d\theta^2+r^2\sin^2\theta d\phi^2$, which …
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How does temperature correspond to number of particles produced?
I'm looking to calculate the number of particles per unit time produced by a Schwarzschild black hole through Hawking radiation. I know that the temperature of the black hole goes as $\kappa/2\pi$, bu …
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1
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Quadrupole moment of Kerr spacetime
In this paper, the Kerr black hole is described as having quadrupole moment of $q=J^2/M$ (which means $q=a^2M$ using $J=aM$) whereas in this paper it says in the abstract that the limiting case of Ker …
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Deriving the Schwarzschild metric in the weak-field regime
I am trying to derive the weak-field Schwarzschild metric, but starting from the same form as Schwarzschild:
$ds^2=-(1+2\Phi(r))dt^2+(1-2\Psi(r))dr^2 +r^2 d\Omega^2$
which has $R=-2\partial_r^2 \Phi …
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What is the physical reasoning for the weak-field approximation to gravity having a curvatur...
The metric for the weak field approximation to gravity is given by
$ds^2 = -(1-\Phi(r))dt^2 + (1+\Psi(r))\left(dr^2 + r^2d\theta^2 + r^2\sin^2\theta d\phi^2\right)$
When $\Phi(r)=\Psi(r)$, e.g. when …