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 ...
6
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2answers
612 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 ...
5
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1answer
211 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 ...
17
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1answer
4k 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 ...
2
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1answer
308 views

What is exactly rotating in a rotating black hole?

I have read this: https://arxiv.org/abs/gr-qc/9404041 In General Relativity the black hole solutions which have so far been found form a four parameter family called the generalized Kerr-...
8
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2answers
930 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 ...
10
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1answer
395 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 ...
3
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2answers
740 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 ...
9
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1answer
268 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 ...
6
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4answers
595 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 Schwarzschild metric of a non-rotating black hole is known inside the ...
2
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1answer
326 views

Metric diameter of a ring singularity

In the Kerr metric the ring singularity is located at the coordinate radius $r=0$, which corresponds to a ring with the cartesian radius $R=a$. So the center of the ring singularity in cartesian ...
11
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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 ...
14
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2answers
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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
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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 ...
8
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1answer
1k 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. ...
5
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2answers
893 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 $|M|>|a|$ (...
8
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3answers
372 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 ...
5
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2answers
568 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". ...
5
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1answer
322 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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1answer
214 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 ...
4
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1answer
333 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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2answers
219 views

What's the inner ergosphere in a Kerr black hole?

(My book uses the notation "ergosphere" as the hypersurface of static limit, "ergoregion" as the hypervolume within.) Studying the Kerr BH, I've come to the part about horizons and ...
2
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2answers
550 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 ...
8
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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 ...
6
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1answer
267 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
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1answer
1k 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 ...
4
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1answer
69 views

Exceeding the Kerr black hole spin limit

It is well known that the limit on the angular momentum for a Kerr black hole is given by \begin{equation} 0 \leq a^* \leq 1 \quad \text{where} \quad a^* \equiv \frac{cJ}{GM^2} \end{equation} and $J$ ...
4
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1answer
698 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 ...
3
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2answers
2k views

Kerr black hole horizons and infinite redshift surfaces

In the Kerr black holes we have infinite-redshift surfaces (where a infalling body is still according to the asymptotic observer) and event horizons (the escape velocity becomes greater than the speed ...
2
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2answers
306 views

For a given mass, how big can a Kerr black hole get?

We know that in a Kerr Black Hole the singularity is in the form of a 1 dimensional ring. If we have a 25 solar mass black hole, how big would the Kerr Ring be, width wise? Also, I read the Wiki on ...
2
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2answers
388 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
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2answers
458 views

What kind of volume does the event horizon of a Kerr black hole enclose?

I'm sorry if this is a naive question, I'm not too good with General Relativity. I'm aware that a rotating black hole is described by the Kerr Metric, and black holes of this kind have ring ...
0
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2answers
131 views

Why can't a particle rotate opposite to the central mass within the ergosphere?

Wiki says about the Kerr metric: A moving particle experiences a positive proper time along its worldline, its path through spacetime. However, this is impossible within the ergosphere, where $g_{...
2
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1answer
130 views

Particle falling into a Kerr black hole

Let's say that a particle starts a radial free fall towards a Kerr black hole with zero initial energy at $r\rightarrow\infty$. The initial angular momentum of the particle is zero ($p_\phi = 0)$. ...
2
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3answers
599 views

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 ...
1
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1answer
281 views

Event horizon of a rotating black hole

For a non-rotating black hole, Schwarzschild radius itself forms the event horizon, but how do we find the event horizon of a rotating Kerr black hole?
1
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1answer
383 views

Free-falling from rest into a Kerr black hole

Is it impossible for a particle (with zero angular momentum) to free-fall from rest at infinity into the ergosphere of a Kerr black hole? It seems like it is very easy to show this is the case, but ...