Questions tagged [kerr-metric]

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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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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 ...
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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 ...
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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)\...
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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
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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 ...
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
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0answers
79 views

Kerr metric in BMS (Bondi-Metzner-Sachs) coordinates

I am trying to put the Kerr metric into the famous Bondi gauge, which is given for instance by the formula (6.2.10) at page 154 of the following paper: https://arxiv.org/abs/1801.01714. Now, Barnich ...
2
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1answer
80 views

Would naked singularities have a complex irreducible mass?

The formula for the irreducible mass, also known as the Christodoulou and Ruffini equation, is $$M_{\rm irr} = \frac{\sqrt{2 M^2-Q^2+2 M \sqrt{M^2-Q^2-a^2}}}{2}$$ where M is the mass equivalent of ...
2
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0answers
244 views

Physical reality of inner event horizon and inner ergosurface in a rotating black hole in D. Wiltshire et al. “The Kerr spacetime”

In chapter 1/The Kerr spacetime-a brief introduction by Matt Visser of D. Wiltshire, M. Visser, S.M. Scott "The Kerr spacetime - Rotating black holes in general relativity" the author presents a ...
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0answers
121 views

Can rotating black hole have toroidal event horizon with penetrating relativistic jet(s)?

It is conjectured that a rotating black hole has at its center a ring-shaped singularity. Thus, at the center of the ring-shaped singularity the gravitational field must be zero (similar to ...
2
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0answers
428 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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0answers
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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0answers
51 views

Zero mass Kerr metric

When mass in Kerr metric is put to zero we have $$ds^{2}=-dt^{2}+\frac{r^{2}+a^{2}\cos^{2}\theta}{r^{2}+a^{2}}dr^{2}+\left(r^{2}+a^{2}\cos^{2}\theta\right)d\theta^{2}+\left(r^{2}+a^{2}\right)\sin^{2}\...
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0answers
98 views

What is the true shape of a black hole?

I’m pretty sure if a black hole is rotating, then it is shaped as an oblate spheroid. But I know that the equations of general relativity tell that instead of having just one radius. In location of ...
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0answers
183 views

Conservation equation of a perfect fluid in Kerr geometry

I am reading a paper in which a perfect fluid in the Kerr geometry is studied. The stress-energy tensor is \begin{equation} T_{\mu \nu} = (\epsilon + P) u_\mu u_\nu + P g_{\mu \nu}, \end{equation} ...
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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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0answers
305 views

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 ...
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243 views

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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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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176 views

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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565 views

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, ...
1
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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
35 views

Derivation of radial momentum equation in Kerr geometry

I am trying to derive the radial momentum equation in the equatorial plane of Kerr geometry obtained by Lasota (1994) which reads (eqn. 6 in page-343; I am using units in which $M=1$) as follows: $$uu'...
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0answers
16 views

Beyond Kerr Carter constant?

What are the most symmetrical black hole spacetimes whose motion is completely integrable with a Carter constant-like and hidden symmetry superintegrability condition? Do type D-spacetimes have a ...
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57 views

Proof that the Kerr metric may be written in orthogonal form

Prove or disprove that the Kerr metric can be expressed in a set of orthogonal coordinates over some coordinate chart. Motivation for this question stems from my understanding that a metric can ...
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33 views

How to get the black hole spin in RPM if you have the value of $a$?

Most research papers use the variable "a" to describe black hole spin, which always has a value of less than 1, I don't know what this variable is called, but from what I know it can't exceed 1 ...
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89 views

Gram-Schmidt Orthonormalization

In the paper from Kulkarni et al., 2011 (Appendix B1), a method is given for transforming from Boyer-Lindquist (BL) coordinates to a comoving frame. This involves using Gram-Schmidt ...
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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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71 views

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 ...