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.
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...
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
$$
J_m =(\sqrt{2}(r−ia\cosθ))^{−1} i(r^2+a^2)\sin(θ)j,
$$
$$
J_n = - \frac{a \Delta}{ 2 \Sigma} \sin(\theta...
A Kerr Black Hole (BH) is a spinning BH. There is an Event Horizon (EH) which is $$r_H^\pm = \frac{r_S \pm \sqrt{r_S^2 -4a^2}}{2}$$ where ##a=\frac{J}{Mc}## and ##r_S## is the Schwarzschild radius. My question is, suppose I'm in a spacecraft, not in orbit, but stationary at a distance ##r##. I...
Hi all:
As stated in the summary I'm in need for bibliography about timelike geodesics in the Kerr metric.
I have tried using the "Mathematical Theory of Black Holes" by S. Chandrasekhar but I find it a bit to complex.
Is there any other good books or articles about this that you might know...
Just as the time dilation formula for the Schwarzschild metric in terms of the position ##r## away from center of mass for a gravitational body and the Schwarzschild radius ##r_s = {2GM}/{c^2}## is given by
$$ \tau = t \sqrt{1 - \frac{r_s}{r} } $$
so I'd like to know the corresponding...
Compute the Komar integral for the Kerr metric
\begin{equation*}
J=-\frac{1}{8 \pi G} \int_{\partial \Sigma} d^2 x \sqrt{\gamma^{(2)}} n_{\mu} \sigma_{\nu} \nabla^{\mu} R^{\nu}
\end{equation*}
The Kerr metric is given by
\begin{align*}
(ds)^2 &= -\left(1-\frac{2GMr}{\rho^2} \right)(dt)^2...
I am trying to derive the radial momentum equation in the equatorial Kerr geometry obtained from the equation $$ (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...
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 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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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}...
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...
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...
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 = -...
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)...
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...
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.
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...
"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 ...
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...
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?