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Questions tagged [kerr-metric]

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28
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2answers
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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 ...
15
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1answer
3k views

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 ...
12
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2answers
427 views

How does the Penrose diagram for a spinning black hole differ in realistic scenarios (formed by stellar collapse)?

The Penrose diagram for a non-spinning Schwarzschild black hole is Notably, there is a second universe "on the other side" of the black hole. However, actual black holes form by stellar collapse, and ...
10
votes
4answers
3k views

Surface gravity of Kerr black hole

I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand. Firstly, the metric is given by $$\mathrm{d}s^...
10
votes
1answer
351 views

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 ...
10
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3answers
1k views

Closed timelike curves in the region beyond the ring singularity in the maximal Kerr spacetime

The region beyond the ring singularity in the maximal Kerr spacetime is described as having closed timeline curves. Why and/or how is the question. Now if you look a Kruskal-Szkeres Diagram (or a ...
10
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3answers
473 views

Physical motivation for mathematically extending solutions to Einstein's equations

Sorry if this question gets a little long; I want to explain why I'm asking it. The usual Schwarzchild metric $$ds^2 = -\left(1-\frac{2M}{r}\right) dt^2 + \left(1-\frac{2M}{r}\right)^{-1} dr^2 + r^2(...
8
votes
1answer
2k views

Is it expected that all stellar black holes will be spinning near the maximum allowed $\omega$-velocity?

Using a bit of classical reasoning I'm imagining black hole formation to be much like an ice skater pulling in her arms: Now, the size difference between a star and its black hole can't even be ...
8
votes
1answer
731 views

Killing tensor in the Kerr metric

It was famously shown by Carter that the Kerr metric possesses a 4th non-obvious constant of the motion, derived from the separability of the Hamiltonian. This constant is related to a Killing tensor. ...
8
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1answer
191 views

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 ...
7
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2answers
3k views

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 ...
7
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2answers
702 views

Kerr Metric in Orthogonal form

I've seen the Kerr metric usually presented in the Boyer-Lindquist coordinates where there is a cross term in the $d\phi$ and $dt$ term. I've done a good bit of searching and cannot find any ...
7
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2answers
487 views

Escape velocity from a rotating black hole

Under Newton, the escape velocity is $$v_{esc} = \rm c \ \sqrt{r_s/r}$$ where $\rm r_s=2 \ GM/c^2$. In the nonrotating relativistic case (the Schwarzschild case) the radial escape velocity is the ...
7
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1answer
1k views

Kerr geodesics differential equations in equatorial plane

With friend, we are writing an interactive educational simulation of particle falling into a black hole. Currently we use Schwarzschild geodesics. However, we want to generalize it to the case of ...
7
votes
2answers
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 ...
7
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3answers
250 views

Is there a Birkhoff-like theorem for stationary axisymmetric metrics?

I know about the theorem by Robinson and Carter about the uniqueness of the Kerr metric in the case of stationary axisymmetric (SA) black holes. Are there any uniqueness theorems like Birkhoff's ...
7
votes
3answers
590 views

Why is the photon-sphere around a Kerr Black Hole spherical and not ellipsoid?

Kerr Black Holes have usually (excluding extrema $a=0$, $a=1$) due to their spinning activity an ellipsoidal ergosphere. So why does the photon-sphere does not have an ellipsoidal form? On the ...
6
votes
2answers
221 views

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 ...
6
votes
1answer
251 views

Charged versus rotating black holes as different kinds of wormholes

I've heard that a maximally extended charged black hole can be a traversable wormhole to the same universe whereas a maximally extended uncharged rotating black hole can only be a wormhole to ...
5
votes
1answer
207 views

Torsion in kerr black holes

In General Relativity, we generally assume that the derivative operator is torsion-free, i.e., second covariant derivatives commute on functions. However, in Kerr black holes, spacetime is dragged (...
5
votes
1answer
119 views

Gravitational lensing redshift around a Kerr black hole

Light from a source passes by a Kerr black hole on two sides at the equator and converges at the observer. The axis of rotation of the black hole is perpendicular to the direction of light. Two rays ...
5
votes
1answer
252 views

Particle crossing the outer event horizon of a Kerr black hole

I am quite puzzled by the following statement in Sean Carroll's 'Spacetime and geometry' (formula 6.100). A particle with momentum $p^\mu$ crossing the outer event horizon of a Kerr black hole $r=...
5
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2answers
492 views

Closed timelike curves in the Kerr metric

I just read in Landau-Lifshitz that the Kerr metric admits closed timelike curves in the region $r \in (0, r_{hor})$ where $r_{hor}$ is the event-horizon ( I am talking about the case $|M|>|a|$ (...
5
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1answer
192 views

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 ...
5
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0answers
91 views

de-Sitter spacetimes

In classical textbooks for GR, Schwarzschild and Kerr spacetimes are adequately described. In which books or articles, it is mostly believed that Reissner-Nordstrom, Kerr-Newman, Schwarzschild-de ...
5
votes
4answers
501 views

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 ...
4
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2answers
259 views

Is a stable orbit possible inside the ergosphere of a Kerr (spinning) black hole?

I have heard that it's "impossible to hover" inside of an ergosphere, but everywhere I read this seemed to be speaking in the context of "relative to a stationary observer outside of the ergosphere". ...
4
votes
1answer
283 views

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 ...
4
votes
1answer
108 views

Metric for a rotating star

If we want to describe a static spherically symmetric star we can use a metric which matches the Schwarzschild solution with correct mass on the outside of the star but differs from Schwartzschild in ...
4
votes
1answer
150 views

Kerr Black hole EH and Ergosphere embedding

Goodmorning everyone. I would like to share with you a question that has been gripping me for some time, but which I have never been able to give a convincing answer. When representing the ergosphere ...
4
votes
1answer
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 \...
4
votes
1answer
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 ...
3
votes
1answer
138 views

What is the Kerr factor for Sagittarius A*?

I have searched for it, but everything what I found is that A0620-00 (the current closest black-hole to Earth) is a slow spinner with Kerr factor $a=0.12$. How about the Kerr factor for Sagittarius A*...
3
votes
2answers
684 views

Ergosphere treadmills

Suppose you place a number of rotating black holes in linear sequence (rotating around the same axis) between two stars at distance $d$ (assume as tightly packed as practical for purposes of ...
3
votes
2answers
70 views

How to derive the angular velocity of circular orbits in Kerr geometry?

I am trying to derive the angular velocity of a circular orbit in Kerr geometry, eqn.(2.16) in Bardeen et al (1972) which reads $$\Omega=\dfrac{1}{r^{3/2}+a}$$ (Note that I am using the units in which ...
3
votes
1answer
91 views

Particle is not at rest with respect to itself around Kerr spacetime?

Assuming a particle is at rest in a certain frame of reference around a kerr spacetime and hence the 4-velocity (in spherical polar coordinates) of the particle is given by $$ u=(u^{t},0,0,0)$$ Now, ...
3
votes
1answer
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 ...
3
votes
1answer
60 views

Physical significance of angular velocity of orbits around Kerr black holes

For the Kerr metric $$ds^2=\left(g_{tt}-\frac{g_{t\phi}^2}{g_{\phi\phi}}\right)dt^2+g_{\phi\phi}\left(d\phi-\omega dt\right)^2+g_{rr}dr^2+g_{\theta\theta}d\theta^2$$ the angular momentum is defined as ...
3
votes
1answer
593 views

What is really going on in the ergosphere of a Kerr black hole?

Considering the Kerr metric with $GM>a$, we can compute 2 event horizons: $r_\pm=GM\pm \sqrt{G^2M^2-a^2}$ These event horizons are null surfaces, and trajectories are timelike between $r_+$ and $...
3
votes
3answers
477 views

Why is the mass of a Kerr black hole proportional to its angular momentum?

I'm a third year mathematics undergrad, and have just started the module General Relativity and spacetime geometry, I also have a keen interest in black holes. However I would like to know why and ...
3
votes
1answer
122 views

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-...
3
votes
0answers
224 views

Periodicity trick for Kerr Black Holes

I am slightly confused concerning the euclidean section of a Kerr black hole. In page 5 of the following paper https://arxiv.org/abs/hep-th/9908022 it is said that in order to get the euclidean ...
3
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0answers
157 views

Derivation of Equation of Trajectory around a Kerr Black Hole

I was trying to derive equation of motion for test particle around a Kerr black hole. My work is as follows: The Kerr metric is as follows $$ \mathrm ds^2 = -\left(1-\dfrac{2Mr}{\rho^2}\right)\...
3
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0answers
197 views

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 ...
3
votes
0answers
461 views

Orbital period and velocity around a Kerr black hole relative to fixed stars

I've been trying to make progress on some of the smaller pieces of this question about the environment around a Kerr black hole. In order to calculate the effects of special relativistic Doppler shift ...
3
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0answers
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 ...
2
votes
2answers
303 views

Local frame of reference

I am currently simulating particle trajectories in Kerr spacetime numerically with $M=1$ and $a=1$. In the picture above, I am calculating the geodesic in Boyer-Lindquist coordinates. I was messing ...
2
votes
2answers
559 views

Area of the event horizon of a rotating black hole

The Kerr metric for a black hole of mass $M$ and angular momentum $J = aM$ is $$ds^{2} = - \frac{\Delta(r)}{\rho^{2}}(dt-a\sin^{2}\theta d\phi)^{2} + \frac{\rho^{2}}{\Delta(r)}dr^{2} + \rho^{2} d\...
2
votes
4answers
155 views

Visualization of $ dtdx$ and $dxdy$ term in metric tensor

For the sake of simplicity, lets take a 2+1 dimensional spacetime. Lets take the metric $$ds^2 = g_{tt}dt^2 + g_{xx}dx^2 + g_{yy}dy^2 + g_{tx}dtdx + g_{xy}dxdy$$ What is the visualization or ...
2
votes
1answer
71 views

Complex-valued event horizon of a Kerr black hole?

The Kerr metric has two physical relevant surfaces on which it appears to be singular. Solving the quadratic equation $1/g_{rr} = 0$ yields the solution: $$r_H^\pm=\frac{G M}{c^2}\pm\sqrt{\left(\frac{...