# Questions tagged [kerr-metric]

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102 questions
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### $g^{\mu \nu}$ (inverse metric) for Kerr metric in ingoing Kerr coordinates

I need to do a calculation in ingoing Kerr coordinates. I have $g_{\mu\nu}$ from which $g^{\mu\nu}$ can be obtained by hand. However there are so many terms and the final result is not in good form. ...
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### Killing vector $\xi_\alpha$ at event horizon of Kerr black hole

I am calculating surface gravity of Kerr Black Hole following 'A Relativist's toolkit' which uses the definition $$\left(-\xi^\beta \xi_\beta\right);_\alpha=2\kappa \xi_\alpha$$ where $\kappa$ is ...
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### In what coordinates is the following Kerr metric writing in?

In this book the kerr metric was given by I am confused because of the appearance of the $2d\nu dr$ term because in the standard Kerr metric I know this term doesn't appear. Does anyone know what ...
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### Ring singularity of Kerr metric

I have been reading about the Kerr metric using various sources (Wald's textbook, Visser's The Kerr spacetime: A brief introduction etc.). I could not understand exactly why the singularity structure ...
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### Binary black hole merger viewed from inside the event horizon

How did the metric evolve inside the event horizons of the black holes whose merger caused the GW150914 signal? In principle the Schwarzchild metric of a non-rotating black hole is known inside the ...
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### Kerr spacetime and Carter time machine

In the Boyer-Lindquist-Block III (inside the inner event horizon) exists the so-called Carter time machine. There we can show that for every two points $p,q$ there exists a future-pointing timelike ...
2answers
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### Gravitational mass defect

In nuclear physics we have a mass defect by the binding energy of the nuclides. A similar effect appears in the theory of gravitation induced by the gravitational binding energy, which reduces the ...
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### Time independent Kerr metric

The Kerr metric expressed in terms of polar coordinates $r,\theta,\phi$, such that $x = r\sin(\theta)\cos(\phi)$, $y = r\sin(\theta)\sin(\phi)$, $z = r\cos(\theta)$. Then the Kerr metric is given as \...
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### Sources for black hole geodesic orbits

I am looking for good sources that discuss both Kerr and Schwarzschild particle orbits (geodesics). Most sources write down the geodesic equations, constants of motion and the Hamiltonian, but do not ...
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### Effective potential kerr solution

In Newtons mechanic we obtain $E=V_{eff}(r)+\frac{1}{2}mv²$ with $V_{eff}(r)=V(r)+\frac{1}{2} \frac{L²}{mr²}$ for the effectiv potential. The first equation is easy to interpret the total energy ...
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### Total angular velocity (Kerr metric)

I have a problem with the kerr metric and the "rotating spacetime" in the ergosphere. How can i calculate the angular velocity $\omega$ of an object in the ergosphere (which flys from infinity into ...
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### Kerr throat solution derivative

I'm going through this article, since I'll need a part of it for my thesis. And I am trying to derive the Kerr throat solution, from which I should be able, with the change of coordinates get to near-...
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### Multipolar expansion profile of Hawking radiation on Kerr black holes

I would be very curious if Kerr black holes emit Hawking radiation at the same temperature in the equatorial bulges and in their polar regions. I've been looking some reference for this for a couple ...
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### Kerr solution for finite collapse time

The Kerr black hole solutions gives an analytic continuation that is asymptotically flat. Some people have argued that this is another universe, but others state that the analytic continuation ...
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### Boundary conditions for fields in Kerr/CFT

I am reading a paper by Guica et al. on Kerr/CFT correspondence (arXiv:0809.4266) and I'm not sure if I got this. They choose the boundary conditions, like a deviation of the full metric from the ...