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Questions tagged [kerr-metric]

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ZAMO's trajectory near a Kerr Black Hole?

sorry for the "generic" question, just that the last month I have been studying GR from 0 and having problems understanding some of the concepts. Anyways, to the question I wanted to ask: From my ...
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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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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-...
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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 ...
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Effective potential for Kerr geometry

In the review Foundations of Black Hole Accretion Disk Theory, the authors defines an effective potential for Kerr geometry as (Chap. 2, eqn. 23) $$\mathcal{U}_{eff}=-\frac{1}{2}\ln\left|g^{tt}-2lg^{t\...
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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 ...
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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 ...
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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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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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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 ...
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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 ...
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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 ...
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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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Simulating a Test Particle in a Kerr Spacetime $(M,\mathcal{O}, \mathcal{A},\nabla^{L.C.})$

The equations of motion for a test particle in a Kerr spacetime $(M,\mathcal{O}, \mathcal{A},\nabla^{L.C.})$ are dictated by four degrees of freedom (i.e. invariant mass $m$ in $p^\mu g_{\mu\nu}p^{\nu}...
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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 ...
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Numerical Solutions for Equatorial Orbits in the Kerr Black Hole

Currently, I am trying to find timelike orbits in the Kerr metric around the equator. The problem is that no matter which parameters I choose or the method I use I can't seem to get to physically ...
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Light-like normal vectors

Can someone please show me how to mathematically establish that the normal vector to the event horizon of a Kerr Black Hole is light-like?
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How to compute Kerr geodesics?

How would I start to numerically compute trajectories of Kerr geodesics with constants of motion like in this wikipedia page. I want to recreate trajectories like in this picture in Matlab.
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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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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 ...
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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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Quadrupole moment of Kerr spacetime

In this paper this paper, the Kerr black hole is described as having quadrupole moment of $q=J^2/M$ (which means $q=a^2M$ using $J=aM$) whereas in this paper it says in the abstract that the limiting ...
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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 ...
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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". ...
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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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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\...
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Can anyone tell me how can draw shadow of black hole like in presented in Intersteller movie? Is there any code for it in Mathematica or in Python? [closed]

Equation of motion for photon $$ \Sigma \frac{dt}{d\lambda} = aL\left(1-\frac{r^2+a^2}{\Delta}\right) + \omega\left(\frac{\left(r^2+a^2\right)^2}{\Delta}-a^2 \sin ^2\theta\right)\ , $$ $$ \Sigma\frac{...
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The Killing vector $\chi=\partial_t+\Omega_H\partial_\phi$ doesn't look normal to the Killing horizon for a Kerr BH

As mentioned in Carroll's Spacetime and Geometry p. 244, a Killing vector is normal to its Killing horizon. With some help from the other forum, I could check this is true. (FYI, here the Killing ...
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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 ...
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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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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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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 ...
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Centrifugal force on spinning black hole?

I saw the term spinning black hole popping up everywhere so my question do spinning black hole behave similarly to say a planet where it bulge in the equatorial and compress at the poles? what ...
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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 ...
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What would happen to the Earth, if the moon was a black hole? [closed]

Would it be a feasible scenario? I have read this question: What would happen to the Moon if Earth is turned into a black hole? Where Lubos Motl says: The extremal Kerr J=GM2/c∼RbhMc. Now, the ...
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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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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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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 ...
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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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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 ...
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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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1answer
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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, ...
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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
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Can centrifugal force overcome other forces (in a singularity/Kerr metric)?

I have read these questions and answers. None of them answered my question. Typical rotation speeds for black holes Is there a physical upper limit on how fast a physical object can rotate? ...
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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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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{...
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1answer
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Is a Kerr ring singularity a closed string?

I’m obviously not a scientist, but has anyone considered that a Kerr ring singularity might basically be a closed string? The singularity spins in one direction only and is incredibly flat and thin (...
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What is the escape velocity in the Kerr metric? [duplicate]

In the non-rotating Schwarzschild metric there is a straightforward expression for the escape velocity in the radial direction, defined from the point of view of a stationary observer at that radius, ...
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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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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 ...