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Questions tagged [kerr-metric]

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The physical meaning of the cross-term of Kerr metric

I have been experimenting with different types of metric tensors in General Relativity. I decided to try my hand with the Kerr Metric. When I did, I found an odd term in it: namely, a cross product of ...
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Schwarzschild black hole

If law of conservation of angular momentum holds good then how is it possible for a Schwarzschild black hole to exist? Say the momentum of the star initially before the supernova was 1000 kg m/s. Now ...
162 views

How fast does a black hole spin? [duplicate]

When a star dies it explodes in a supernova. This happens when heavier elements like iron is fused in the core of the star. Then the star collapses under its own gravity. This leaves a black hole ...
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Do black holes have a moment of inertia?

My question is in the title: Do black holes have a moment of inertia? I would say that it is: $$I ~\propto~ M R_S^2,$$ where $R_S$ is the Schwarzschild radius, but I cannot find anything in the ...
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What coordinates are used to transform these metrics?

From reading different texts on kerr metric it seem that the kerr metric can be written in two different metrices Kerr metric and Kerr metric Does anyone know what coordinate change can be used to ...
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Does Kerr metric have Hawking temperature?

Does Kerr metric with zero charge have Hawking temperature? What is it given by? I am reading a paper about and it says that the Einstein-Maxwell-Dilaton-Axion black hole and it says that temperature ...
221 views

$g^{\mu \nu}$ (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. ...
225 views

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 ...
290 views

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 ...
799 views

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 ...
433 views

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 ...
297 views

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 \...
119 views

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 ...
134 views

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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Derivation of Kerr metric, is there any reference?

In studying general relativity, many text deals with the derivation of Schwarzschild metric starting from generic metric form. After that impose static, spherical symmetry and obtain the desired ...
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What is the maximum time dilation factor when orbiting a rotating black hole?

Suppose one spaceship is stably orbiting a rotating black hole and another is far away from the black hole. What is the maximum time dilation factor between the two ships? Can it be made arbitrarily ...
140 views

Path of light in Kerr metric? [closed]

How can one find the trajectory of light in various direction in the Kerr metric? Just wondering if there are some classes of solutions, I don't need exact formula. Are there different classes than ...
359 views

What happens to a particle in the exact center of a Kerr black hole?

Kerr black holes (and Kerr-Newman black holes), instead of the "point" singularity theorized in spherically symmetric black holes, instead have a "ring" singularity, spread along the equatorial plane ...
525 views

Geodesics in Kerr

I'm interested in plotting the trajectories of null geodesics near an uncharged rotating black hole (described by the Kerr solution) which involves a system of first order differential equations. Kerr ...
137 views

Where is the way on a rotating black hole to another Universe? [closed]

Where is the way on a rotating black hole to another Universe? Where and how should it be entered by to get away from here?