Kerr Definition and 96 Threads

KERR (750 AM, "KERR Country") is a radio station licensed to serve Polson, Montana. The station is owned by Anderson Radio Broadcasting, Inc. It airs a country music format.The station was assigned the KERR call letters by the Federal Communications Commission.KERR is Montana's primary entry point station for the Emergency Alert System.

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  1. C

    I Line element in Kerr coordinates at singularity

    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...
  2. Haorong Wu

    A Propagation Vector of Light in Kerr Spacetime: Reference Needed

    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...
  3. malawi_glenn

    A (paper) Stability properties of Kerr BH's

    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...
  4. S

    A Units of Kerr Understanding Mass & Angular Momentum

    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...
  5. G

    I Spin (or not) of a Kerr Black Hole

    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...
  6. CanoJones

    I Kerr Metric Bibliography: Resources for Timelike Geodesics

    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...
  7. ergospherical

    Insights Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes

    Continue reading...
  8. Dukon

    A Kerr Metric Time Dilation Formula: Deriving Absolute Form

    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...
  9. E

    I Components of *J in Kerr geometry

    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...
  10. E

    I Finding the angular momentum of a Kerr black hole

    [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...
  11. JD_PM

    Getting a conserved charge out of the Kerr metric

    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...
  12. Marilyn67

    I Unravelling the Mysteries of the Kerr Black Hole Ergosphere

    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...
  13. JD_PM

    A Understanding Kerr Black Holes: Metric, Killing Vectors & Event Horizons

    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...
  14. PeterDonis

    Insights Intro to Centrifugal Force Reversal in Kerr Spacetime

    Continue reading...
  15. E

    A Kerr Black Hole Angular Momentum Limit

    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...
  16. JTorn

    Why doesn't a real Infinite Redshift Limit occur at R+ for Kerr BHs?

    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...
  17. abby11

    A Derive Radial Momentum Eq. in Kerr Geometry

    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...
  18. Creedence

    I Appearance of a Kerr black hole from above

    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.
  19. PeterDonis

    Insights Fermi-Walker Transport in Kerr Spacetime - Comments

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

    Find the Tetrad for Kerr Metric: Step-by-Step Guide

    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
  21. PeterDonis

    A Extra Killing Vector Field in Kerr Spacetime?

    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...
  22. E

    B Solving the Kerr metric in the program Maxima

    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...
  23. Dale

    I Kruskal–Szekeres coordinates for Kerr metric

    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...
  24. S

    A Kerr-Bolt Spacetime: Derivation & Resources

    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.
  25. S

    Polar plot for the event horizon of a Kerr BH

    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...
  26. J

    A Compute Induced Metric on Kerr Event Horizon

    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[...
  27. Conclaude

    Numerical Plot of Particle Orbits in Kerr Equatorial Plane

    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...
  28. G

    Electronically Change Material Refractive Index

    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
  29. M

    Kerr Diagrams for Defect Frequencies

    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...
  30. Mihai_B

    A Kerr-Newman Metric Correction from Einstein-Rosen

    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...
  31. B

    Insights Orbital Precession in the Schwarzschild and Kerr Metrics - Comments

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

    I Inside Black Holes: Unraveling the Kerr Metric Structure

    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...
  33. A

    A How Does the Penrose Process Allow for Energy Extraction from a Black Hole?

    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...
  34. N

    How Can Electrons Move to Higher Shell Levels Without Light Absorption?

    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...
  35. Rlam90

    Two-mass Schwarzschild metric instead of Kerr metric?

    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...
  36. m4r35n357

    Sign of Kretschmann Scalar in Kerr Metric

    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...
  37. m4r35n357

    "Simple" 4D Kerr Geodesics simulator, source code and docs

    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...
  38. D

    Twin Paradox in Kerr Metric - Help Needed

    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...
  39. L

    Kerr metric and rotating stars

    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...
  40. E

    What Does a Rotating Mass in Kerr Metric Rotate With Respect To?

    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...
  41. C

    Penrose Diagram for the Kerr Black Hole

    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...
  42. Lamdbaenergy

    Mass Inflation Instability in Kerr and Reisnerr black holes.

    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.
  43. ShayanJ

    Kerr & Kerr-Newman Solutions in Straumann's GR

    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...
  44. Ganesh Ujwal

    Surface gravity of Kerr black hole

    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...
  45. J

    Equation for time dilation of body in orbit around Kerr black hole?

    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...
  46. T

    Observing Kerr Singularity: What Would an Observer See?

    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...
  47. F

    Orbits around a Schwarzschild/Kerr black hole

    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...
  48. V

    Surface gravity (Killing vecotrs) of 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...
  49. Philosophaie

    Is energy and mass extraction possible within the Kerr Black Hole Ergosphere?

    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...
  50. Philosophaie

    Angular Momentum of Kerr Black Hole

    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 −...
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