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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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2answers
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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 ...
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1answer
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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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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 ...
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1answer
44 views

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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0answers
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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 ...
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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. ...
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0answers
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 ...
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1answer
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 ...
3
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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 ...
2
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1answer
336 views

Killing Horizon for Kerr Black Hole

I have some confusion about Killing Horizon of BH. Since a Killing Horizon (KH) is a null hyper-surface at which killing vector $k^{\mu}$ is null; $k^{\mu}k_{\mu}=0.$ For time translation symmetry $...
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2answers
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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 ...
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0answers
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Kerr Metric and Asymptotically Static Frame

Suppose we are given a Kerr spacetime (e.g. containing a single uncharged rotating black hole). How does one know that the coordinates chosen is rotating or non-rotating as seen from infinity? And how ...
2
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1answer
1k 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 ...
5
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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 (...
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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 ...
5
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2answers
491 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 $|M|>|a|$ (...
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0answers
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Complex tetrad vs. Real metric

I asked this question almost a month ago on mathoverflow (https://mathoverflow.net/q/228138/) but received no response. I thought I could have better luck here: I have a question on the relationship ...
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0answers
429 views

Effective potential for Kerr incorrect?

I am self-learning GR. Background I have been following Christopher Hirata's lecture notes on Kerr geodesics. In Equation 38, the effective potential $V(r)$ is given by: $V(r)=(1-\epsilon)^2r^4-2Mr^...
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4answers
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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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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 $...
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Easy unit conversion in Kerr metric

I would like to use Kerr metric in Boyer-Lindquist coordinates in geometrized units with mass of the black hole normalized to $M=1$. I am embarrassed to admit, but I can't seem to figure out how to ...
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1answer
185 views

Time dilation at the Innermost Stable Circular Orbit

According to general relativity the time dilation is given by following formular: $d \tau = \sqrt{g_{\mu \nu} \dot{x^{\mu}} \dot{x^{\nu}}}$ If I'm interestet in the time dilation at the ISCO I set $...
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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 ...
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2answers
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 ...
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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 \...
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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 ...
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94 views

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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0answers
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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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3answers
707 views

How to get null tetrad by metric?

How to get null tetrads ${l^a,n^a,m^a,\overline{m}^a}$ for this metric? This on is from Ryder's book (Introduction to general relativity) page 268 $g^{\mu\nu}=\begin{pmatrix} 0 & \frac{1}{c} &...
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1answer
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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 ...
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3answers
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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(...
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3answers
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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 ...
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2answers
378 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 ...
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1answer
194 views

Spinning micro blackholes power conversion

In the context of energy extraction of spinning black holes, there are two known mechanisms: the Penrose process and the Blandford-Znajek process. The former relies on fragmentation of accreting flow, ...
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0answers
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How does a rotating black hole look like? How would it be to descend into one?

This image from Wikipedia shows how a black hole would look like: A black circle that acts as a gravitational lens for light rays coming from behind. How would a rotating black hole look like? How ...
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1answer
313 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 ...
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3answers
588 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 ...
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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*...
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4answers
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Kerr metric Christoffel symbols

I've been slaving away trying to calculate the Christoffel symbols for the Kerr metric. Does anybody know of a link that I could compare my answers to? I've done some Google searches and all I can ...
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0answers
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Boyer–Lindquist coordinates

In the Kerr solution to the vacuum Einstein Equation written in Boyer–Lindquist coordinates. Because it is not spherical polar coordinates, $r$ ranges from 0 to infinity does not cover all the space, ...
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2answers
116 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_{...
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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 ...
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1answer
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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 ...
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0answers
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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 ...
7
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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 ...
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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 ...
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1answer
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?
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3answers
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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 ...
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1answer
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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 ...