Kerr Definition and 96 Threads

From paper 'A brief introduction to Kerr spacetime' ( https://arxiv.org/pdf/0706.0622 ) setting m->0 in the line element in Kerr coordinates gives, equation 7 : $$ \text{d}s_0^{2} = -\left( \text{d}u + a\sin^{2}\theta \text{d}\phi \right)^{2}+2\left( \text{d}u + a\sin^{2}\theta \text{d}\phi...

Hi, there. I am currently reading the paper, Gravitational Faraday rotation induced by a Kerr black hole (https://doi.org/10.1103/PhysRevD.38.472). After Eq. (2.4), it reads that The paper does not provide the derivation of the equations and no related reference is listed. Also, ##k^i## is not...

Have these articles been discussed here previously? I could not find it but my search skills suck. Kerr stability for small angular momentum https://arxiv.org/abs/2104.11857 (just 800 pages) Recently (31th May this year) Wave equations estimates and the nonlinear stability of slowly rotating...

I was reading this paper, and I got confused: https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-31/issue-2/The-four-laws-of-black-hole-mechanics/cmp/1103858973.pdf It discusses the Kerr solution for the case of { M4 > J2 } where M is mass & J is angular momentum...

The Kerr solution describes the gravitational field of a rotating black hole. Oftenly, the hole is said to be „spinning“, what appears as misleading to me. My questions: 1.) Is it correct to say that angular momentum in this way is treated like orbital angular momentum, not like spin? 2.) Can...

Hi all: As stated in the summary I'm in need for bibliography about timelike geodesics in the Kerr metric. I have tried using the "Mathematical Theory of Black Holes" by S. Chandrasekhar but I find it a bit to complex. Is there any other good books or articles about this that you might know...

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Just as the time dilation formula for the Schwarzschild metric in terms of the position ##r## away from center of mass for a gravitational body and the Schwarzschild radius ##r_s = {2GM}/{c^2}## is given by $$ \tau = t \sqrt{1 - \frac{r_s}{r} } $$ so I'd like to know the corresponding...

I am in the middle of a problem for the Kerr geometry, I need to do the integral ##\int_{\mathcal{N}} \star J## over a null hypersurface ##\mathcal{N}## which is a subset of ##\mathcal{H}^+##, where ##J_a = -T_{ab} k^b## and the orientation on ##\mathcal{N}## is ##dv \wedge d\theta \wedge...

[Mentor Note -- Specialized question moved to the general technical forums] Homework Statement:: To show that ##J = Ma## for the charged Kerr metric [Wald Ch. 11 Pr. 6] Relevant Equations:: \begin{align*} \mathrm{d}s^2 = &- \left( \frac{\Delta - a^2 \sin^2{\theta}}{\Sigma}\right) \mathrm{d}t^2...

Compute the Komar integral for the Kerr metric \begin{equation*} J=-\frac{1}{8 \pi G} \int_{\partial \Sigma} d^2 x \sqrt{\gamma^{(2)}} n_{\mu} \sigma_{\nu} \nabla^{\mu} R^{\nu} \end{equation*} The Kerr metric is given by \begin{align*} (ds)^2 &= -\left(1-\frac{2GMr}{\rho^2} \right)(dt)^2...

I have a problem understanding what is going on in the region called the ergosphere of a "fast" Kerr black hole. - Relativity teaches us that no frame of reference can have relative displacements greater than the speed of light, ok. - The ergosphere of a fast Kerr black hole can contain light...

Before explicitly stating the Kerr metric let us discuss a bit what to expect, comparing it to the easiest solution to (in-vacuum) Einstein's equations that I know: the Schwarzschild metric. I studied that the Schwarzschild metric is derived under the following assumptions: the metric must be...

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The Schwarzschild metric seems to model, for example, the earth’s gravity field above the earth’s surface pretty well, even though the Earth is not really a golf-ball sized black hole down at the center. Can the same be said for the Kerr metric? Does it model a rotating extended body’s gravity...

As I have studied before, I found that Infinite Red Shift occurs where gtt = 0 but this exercise says that on Kerr's Black Hole it doesn't really work like that. Right now I'm blocked because I didn't find anything on the internet about it so I don't know how to show this phenomenon. Any help...

I am trying to derive the radial momentum equation in the equatorial Kerr geometry obtained from the equation $$ (P+\rho)u^\nu u^r_{;\nu}+(g^{r\nu}+u^ru^\nu)P_{,r}=0 \qquad $$. Expressing the first term in the equation as $$ (P+\rho)u^\nu u^r_{;\nu}=(P+\rho)u^r u^r_{;r} $$ I obtained the...

How does a Kerr black hole look like from above? Is it the same as a Schwarzschild one? I could not find any convincing visualization for this question. By above I mean from a point r>0 and ϑ=0.

Greg Bernhardt submitted a new blog post Fermi-Walker Transport in Kerr Spacetime Continue reading the Original Blog Post.

how to find tetrad of this metric the tetrad given is this one I m a newly born in General Relativity please help me out how this tetrad is derived

In a recent thread, the following was posted regarding the "no hair" theorem for black holes: In the arxiv paper linked to, it says the following (p. 2, after Theorem 1.1): "Hawking has shown that in addition to the original, stationary, Killing field, which has to be tangent to the event...

Does anyone know how to get Maxima to solve the Kerr metric? I enter the terms for that metric that I found on Wikipedia. It tries to print out the Einstein tensor (covariant, leinstein(true)) and the expressions are so long that it literally locks up my computer. And isn’t the Kerr metric a...

I am having trouble understanding the Kerr metric. One of the things which helped me understand the Schwarzschild metric is the Kruskal–Szekeres coordinates. In particular, the fact that light cones were still at 45 degrees was very helpful, and it was helpful to see that the singularity was a...

I am unable to find any paper or book on Kerr-Bolt solution. I need to know its derivation. Please if anyone can suggest some material on it? I will be very thankful.

I have made graph of event horizon of Kerr black hole by giving simple command of polar plot. The problem is that the point where the event horizon and static limit meets should be along y-axis but instead its on x-axis. I have tried everything but not getting it right. What mistake I am...

Hello there, Suppose ## \Delta = r^2 + 2GMr + a^2## and ## \rho^2 = r^2 + a^2 \cos ^2 \theta ##. The Kerr metric is $$ ds^2 = - (1 - \frac{2GMr}{\rho^2})dt^2 - \frac{4GMar\sin^2 \theta}{\rho^2} d t d \phi + \frac{\rho^2}{\Delta} dr^2 + \rho^2 d \theta^2 + \frac{\sin^2 \theta}{\rho^2} \left[...

Context: In James Hartle's Gravity, pp. 318-319, Example 15.1, he considers the case of a particle that starts falling from infinity into a Kerr black hole, initially with no kinetic energy (e = 1) and initially moving radially (ℓ = 0). The particle's motion is constrained along the equatorial...

Hi, How do I electronically change material refractive index? Is Kerr effect the right way? Is there any good material that have Kerr effect, that can be used in modern gadgets? Is there any gadget/device that use this kind of material? Thanks:) Regards, Grheee

I am currently undertaking a module in Failure Analysis, one topic of which is vibration monitoring of bearings. During this study, the notion of first and second Kerr diagrams as a tool for analysis came up. I have been trying to find additional information on Kerr diagrams; however, outwith...

Einstein (+Rosen) came to the conclusion that they have to change the sign for the energy tensor Tik : "if we had taken the usual sign for Tik, the solution would involve +ε2 instead of -ε2. It would then not be possible, by making a coordinate transformation, to obtain a solution free from...

Bill_K submitted a new PF Insights post Orbital Precession in the Schwarzschild and Kerr Metrics Continue reading the Original PF Insights Post.

I have two questions regarding Kerr black holes, which I am hoping some of you might be able to shed some light on for me. 1. What is the physical significance / meaning of the inner ergosurface, the one beyond the inner horizon ? If considered as a boundary surface, what would it separate from...

Hi everyone, I am a bit confused about the Penrose Process. Let's say a particle with energy E at infinity arrives in the ergoregion of a Kerr black hole and then it decays into two photons. One of them has L_1<0 and E_1<0 and hence it falls towards the singularity, while the other has L_2>0...

Can the Kerr effect have a effect on absorption, and transmission, of the electron.? Also is there any way to make electrons move to higher shell levels, without the electrons getting excited by light, and moving to higher Shell's. Or is light absorption the only way for electrons to move to...

Just a thought... Would there be any implicit differences between (A) a two-body metric where the two central masses are drawn ever further together, with angular momentum included, and (B) the Kerr metric? Angular momentum would still be part of the system, but it would be explained by a more...

This question is motivated by one on stack exchange, and on this paper (which comes across a bit student-y but it claims to have been reviewed, and in any case I have reproduced its results in ctensor and gnuplot). So: the KS (abbreviation!) conveys an overview of curvature at a given point in...

Looks like my main pet GR project is about to enter something akin to maintenance mode, since it now does all I currently need it to. It's nothing earth-shattering at first glance, but is very concise (e.g. ~100 lines of Python for the simulator script) and should be easier to understand than...

Hi. I've been struggling with a formulation of the twin paradox in the Kerr metric. Imagine there are two twins at some radius in a Kerr metric. One performs equatorial circular motion whilst the other performs polar circular motion. They separate from one another and the parameters of the...

I have recently come across the notion that Kerr metric describes the spacetime outside a rotating black hole but not outside a rotating (electrically neutral) star. Unlike Schwarzschild metric, which works both for non-rotating spherically symetric black hole without charge as well as any other...

I understand the Kerr metric has an off-diagonal term between the rotation and the time degrees-of-freedom? That a test mass falling straight down toward a large rotating mass from infinity will begin to pick up angular momentum? Is that what’s called “frame dragging”? Did the Gravity Probe B...

Hey Guys, so i was reading Hawking&Ellis a bit and still encounter always problems with the Penrose-Diagrams. Looking at the Penrose-Diagram for the rotating Kerr-Black hole (just one illustrating picture at the end) i come up the following question: Why are there TWO regions III and III ? In...

What exactly is this mass inflation instability phenomenon that is said to happen near the inner horizon of black holes? http://jila.colorado.edu/~ajsh/insidebh/realistic.html I got the nutshell of it, but I think I need someone to really explain this.

In the book General Relativity by Norbert Straumann, He derives the Kerr's solution in the chapter about black holes and then modifies it to get the Kerr-Newman solution. Then he calculates the g-factor of a rotating charged black hole using the Kerr-Newman solution(and gets the amazing result...

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...

Inspired by the movie Interstellar which featured a planet orbiting a rotating supermassive black hole with an extremely high time dilation factor (slowed by a factor of 60,000 relative to observers far from the black hole), I was wondering if anyone knows of an equation for time dilation of...

I know it is very unlikely such thing exists because QM can prevent CTLs However, what observer would see near such singularity? As ring is timelike, for an observer it won't be a ring at all, but a point, correct? That point should be visible (naked) because there are no horizons between an...

Hi everybody, Around a black hole, a test particle can experience two types precession: of its pericenter and of its angular momentum vector. I would like to know if there exist an EXACT expression for the rate at which these two precession occurs both for a Schwarzschild and a Kerr black hole...

Hello, I am interested in surface gravity of Kerr black hole it means, I need to find killing vector for Kerr which is null on outer horizont. Is it true? How should I do that? I guess it could be some linear combination of vecotrs ∂/∂t and ∂/∂\phi. So can I looking for that this way...

In a Kerr Black Hole there exists a region called the Ergosphere. It is between the Event Horizon and a spheriod called the Static Limit. The Event Horizon can be simplified to: ##\Delta## = 0. The Static Limit can be simplified to: ##g_{tt}## = 0. They yield two separate spheres...

Homework Statement How do you find the Angular Momentum, J, if you are given the Angular Velocity, ω of a Kerr Black Hole. Homework Equations J = I*ω ##I = mass*r^2## Event Horizon: ##r_+ = M + (M^2 − (J/mass/c)^2)^{1/2}## Static Limit and the Ergosphere: ##r_0 = M + (M^2 −...