What is Kerr metric: Definition and 40 Discussions

The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.

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  1. Bertin

    Form of radial velocity along null geodesic under the Kerr metric

    By the symmetries of the metric, k = \partial_t and l = \partial_\phi are Killing vectors. Since they are Killing vectors, they satisfy k_\mu \dot{x}^\mu = E and l_\mu \dot{x}^\mu = L, for the same constants appearing in the expression we must prove, and where the dot means the derivative w.r.t...
  2. Nitacii

    Integrate source terms for test EM field in Kerr spacetime

    Hello, the Homework Statement is quite long, since it includes a lot of equations so I will rather post the as images as to prevent mistypes. We need to find the integral where with $$ J_m =(\sqrt{2}(r−ia\cos⁡θ))^{−1} i(r^2+a^2)\sin⁡(θ)j, $$ $$ J_n = - \frac{a \Delta}{ 2 \Sigma} \sin(\theta...
  3. Vick

    I What are the effects on a stationary observer for Kerr metric?

    A Kerr Black Hole (BH) is a spinning BH. There is an Event Horizon (EH) which is $$r_H^\pm = \frac{r_S \pm \sqrt{r_S^2 -4a^2}}{2}$$ where ##a=\frac{J}{Mc}## and ##r_S## is the Schwarzschild radius. My question is, suppose I'm in a spacecraft, not in orbit, but stationary at a distance ##r##. I...
  4. 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...
  5. 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...
  6. 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...
  7. 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...
  8. 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
  9. 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...
  10. 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...
  11. stevebd1

    Insights Calculating the Spin of Black Hole Sagittarius A* - Comments

    Greg Bernhardt submitted a new PF Insights post Calculating the Spin of Black Hole Sagittarius A* Continue reading the Original PF Insights Post.
  12. S

    I Frame Dragging Direction for Outward Moving Test Mass

    I have the following question considering frame dragging: A test mass starting at rest near a rotating mass or with an initial velocity pointing towards the center of the rotating mass will be deflected in such a way that it begins to move around the mass in the rotational direction. This is...
  13. L

    I Gravitational Waves & Black Holes: Exploring the Connection

    This is something I've been curious for some time. I've heard that there is a relation between gravitational waves and black holes. Moreover, this year the quite important paper "Observation of Gravitational Waves from a Binary Black Hole Merger" was published. Now, I'm starting to study...
  14. 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...
  15. 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...
  16. MattRob

    Validity of Schwarzschild Metric in Real BHs

    So, I've been reading through "Exploring Black Holes: Introduction to General Relativity" by Wheeler and Taylor, and I've had some ideas I wanted to pursue and do some research in regarding trajectories within the event horizon. In this, I'd like to have the mathematical tools to investigate...
  17. J

    Translational Motion Vs. Rotational Motion

    Howdy. It has become clear to me that translational motion is not taken into account in general relativity because it is subjective, and that rotational motion is taken into account in GR in places such as the Kerr Metric. What makes rotational motion so absolute? Couldn't an observer's...
  18. 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...
  19. 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...
  20. E

    Rotation in the Kerr metric?

    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...
  21. Y

    Practical measurements of rotation in the Kerr metric

    In another thread WannabeNewton mentioned: and gave this reference: Until WBN mentioned it, I had never given any thought to the difference between these methods of measuring rotation, so I would like to explore those ideas further here, particularly in relation to the Kerr metric. Consider...
  22. Y

    CTCs in Kerr Metric: Examining the Invariance of CTCs in Spacetime

    Are CTCs in the Kerr metric just an artefact of the coordinates used? This paper http://arxiv.org/abs/gr-qc/0207014 suggests that is the case. In a private message it has been suggested to me that CTCs in a spacetime are an invariant feature so are not removable by a change of coordinate system...
  23. D

    Time Travel - Between two Kerr metric black holes w/detached event horizons

    So imagine your on Earth at a latitude of 30 to 45° N, between two rotating Kerr Metric Blackholes with detached event horizons (dual singularities) allowing you to be shielded from the crushing force of the black holes. Which way do the rotating black holes need to rotate for the past and...
  24. apeiron

    CP violation explained by Kerr metric

    This is an interesting hypothesis that doesn't seem to have been discussed yet. What are its flaws? Mark Hadley at the University of Warwick argues that galactic rotation causes gravitational frame-dragging sufficient to put a local asymmetric twist into spacetime and explain observed CP...
  25. jfy4

    Electron Falling in Kerr Metric: Release of 40% Rest Energy?

    I have here a quote from Hartle's Gravity, page 321: "The fraction of rest energy that can be released in making a transition from an unbound orbit far from an extremal black hole to the most bound innermost stable circular orbit is (1-1/\sqrt{3})\approx 42\%". My question is about...
  26. Y

    How to obtain Kerr Metric via Spinors (N-P Formalism)

    How to obtain Kerr Metric via Spinors (Newman-Penrose Formalism)? I am a bit confused with Ray d'Inverno's Book. Why perform the coordinates transformation: 2r-1 -> r-1 + r*-1 I am bit confused of it. And I am a bit confused, too, of how to write out null tetrad...
  27. L

    Kerr Metric Confusion: Problem 1 on Page 138

    Hi. I'm trying problem 1 on p138 of this http://arxiv.org/PS_cache/gr-qc/pdf/9707/9707012v1.pdf Now when I try and get the Euler Lagrange equation for \phi I get (the Kerr metric in BL coordinates can be found at the bottom of p77) \frac{\partial L}{\partial \phi} = \frac{d}{d \tau}...
  28. I

    Dark matter, dark energy, and the Kerr metric?

    I’m sorry, but I find dark matter and dark energy problematic. It’s hard to think of a Universe made up of about 95 % of stuff we have no idea about, except that maybe dark matter and dark energy have some properties. So I’m thinking maybe there’s something wrong with the data, but I can’t...
  29. Z

    What are physics constant in Kerr metric?

    1. What are the value of physics constant in Kerr metric, including G, M, c, a, r, or others? I expect to simplify Gamma 2. why g_compts[1,4] has element and not [4,1]? 3. Some book assume G = c = 1, what is the meaning of this setting? 4. Different material have different metric, are...
  30. E

    Question about Killing vectors in the Kerr Metric

    Hi, I'm a physics undergrad working through Carroll at the moment. In the section on the Kerr black hole, he states that K= \partial_t is a Killing vector because the coefficients of the metric are independent of t. He then states in eq. 6.83 that K^\mu is normalized by: K^\mu K_\mu = -...
  31. S

    Kerr metric derivation (Adler, Bazin & Schiffer)

    I have a problem understanding part of Adler, Bazin and Schiffer's (Introduction to General Relativity 2nd Edition) derivation of the Kerr metric. I would be grateful if someone could explain where I am going wrong. My problem concerns the transition from the O(m2) equation (7.15b) to (7.24)...
  32. stevebd1

    What is the equation for stable orbits in Kerr metric?

    The equation for the surface gravity of a black hole in Kerr metric is- \kappa_\pm=\frac{r_\pm-r_\mp}{2(r_\pm^2+a^2)} where r+ is the outer event horizon- r_+=M+\sqrt(M^2-a^2), r- is the inner event horizon- r_-=M-\sqrt(M^2-a^2) and a is the spin parameter in metres- a=J/mc. An exact...
  33. U

    How can I easily study the derivation of Kerr Metric?

    Hello friends.I study about Kerr metric and black holes.I can deriving Schwarzschild metric basically but i can't derive the Kerr metric. Anyone know how can i study it with basic concepts? please suggest to me any lecture note or text. thanks.
  34. Jorrie

    Accelerations in Kerr Metric

    Pervect has https://www.physicsforums.com/showpost.php?p=1046874&postcount=17" for radial and tangential gravitational accelerations of a moving particle in Schwarzschild coordinates. \frac{d^2 r}{d t^2} = \frac {3 m{{\it v_r}}^{2}}{ \left( r-2\,m \right) r} + \left( r-2\,m \right)...
  35. R

    Kerr metric, singularities in Boyer-Lindquist and Cartesian coordinates

    I've found a fairly concise review of the Kerr metric at http://www.physics.mcmaster.ca/phys3a03/The%20Kerr%20Metric.ppt The Kerr Metric for Rotating, Electrically Neutral Black Holes: The Most Common Case of Black Hole Geometry. Ben Criger and Chad Daley. On slide 6 they give the usual...
  36. R

    Ring -singularity (Determinant of the Kerr metric)

    "Ring"-singularity (Determinant of the Kerr metric) My problem is as follows: "Calculate the determinant of the Kerr metric. Locate the plac where it is infinite. (In fact, this gives the "ring"-singularity och the Kerr black hole, which is the only one) I got the determinant to ...
  37. Orion1

    Kerr metric hydrostatic equilibrium

    I basically understand how the Tolman-Oppenheimer-Volkoff equation for hydrostatic equilibrium was derived from the Schwarzschild metric in General Relativity and from the equation derivatives listed. However, when I attempt to derive the equation derivatives for the Kerr metric, I obtain these...
  38. Orion1

    Understanding the Kerr Metric: Solving for Delta and Lambda functions

    According to Wikipedia, the equation for the Kerr metric is: c^{2} d\tau^{2} = \left( 1 - \frac{r_{s} r}{\rho^{2}} \right) c^{2} dt^{2} - \frac{\rho^{2}}{\Lambda^{2}} dr^{2} - \rho^{2} d\theta^{2} - \left( r^{2} + \alpha^{2} + \frac{r_{s} r \alpha^{2}}{\rho^{2}} \sin^{2} \theta \right) \sin^{2}...
  39. A

    Can one diagonalize the Kerr metric?

    Is it possible to diagonalize the Kerr metric in the Boyer-Lindquist coordinates? If so then I think calculations with the metric will become easier. I forget under what condition a matrix can be diagonalized. Can anybody remind me?
  40. V

    Finding a Kerr Metric Using the Einstein Equation

    How can I obtain a Kerr metric by using the Einstein equation?