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2
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3answers
95 views

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? ...
5
votes
1answer
102 views

Charged versus rotating black holes as different kinds of wormholes

I've heard that a maximally extended charged black hole can be a traversable wormhole to the same universe whereas a maximally extended uncharged rotating black hole can only be a wormhole to ...
2
votes
1answer
85 views

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 ...
1
vote
1answer
88 views

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 + ...
1
vote
1answer
170 views

Spinning micro blackholes power conversion

In the context of energy extraction of spinning black holes, there are two known mechanisms: the Penrose process and the Blandford-Znajek process. The former relies on fragmentation of accreting flow, ...
0
votes
1answer
57 views

Time dilation at the Innermost Stable Circular Orbit

According to general relativity the time dilation is given by following formular: $d \tau = \sqrt{g_{\mu \nu} \dot{x^{\mu}} \dot{x^{\nu}}}$ If I'm interestet in the time dilation at the ISCO I set ...
0
votes
1answer
83 views

How to get null tetrad by metric?

How to get null tetrads ${l^a,n^a,m^a,\overline{m}^a}$ for this metric? This on is from Ryder's book (Introduction to general relativity) page 268 $g^{\mu\nu}=\begin{pmatrix} 0 & \frac{1}{c} ...
3
votes
0answers
78 views

Effective potential for Kerr incorrect?

I am self-learning GR. Background I have been following Christopher Hirata's lecture notes on Kerr geodesics. In Equation 38, the effective potential $V(r)$ is given by: ...
3
votes
0answers
41 views

Sources for black hole geodesic orbits

I am looking for good sources that discuss both Kerr and Schwarzschild particle orbits (geodesics). Most sources write down the geodesic equations, constants of motion and the Hamiltonian, but do not ...
2
votes
0answers
52 views

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 $|M|>|a|$ ...
2
votes
0answers
55 views

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 ...
2
votes
0answers
90 views

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 ...
1
vote
0answers
23 views

Orbital period and velocity around a Kerr black hole relative to fixed stars

I've been trying to make progress on some of the smaller pieces of this question about the environment around a Kerr black hole. In order to calculate the effects of special relativistic Doppler shift ...
1
vote
0answers
57 views

Complex tetrad vs. Real metric

I asked this question almost a month ago on mathoverflow (http://mathoverflow.net/q/228138/) but received no response. I thought I could have better luck here: I have a question on the relationship ...
1
vote
0answers
30 views

Effective potential kerr solution

In Newtons mechanic we obtain $E=V_{eff}(r)+\frac{1}{2}mv²$ with $V_{eff}(r)=V(r)+\frac{1}{2} \frac{L²}{mr²}$ for the effectiv potential. The first equation is easy to interpret the total energy ...
1
vote
0answers
28 views

Total angular velocity (Kerr metric)

I have a problem with the kerr metric and the "rotating spacetime" in the ergosphere. How can i calculate the angular velocity $\omega$ of an object in the ergosphere (which flys from infinity into ...
1
vote
0answers
108 views

How does a rotating black hole look like? How would it be to descend into one?

This image from Wikipedia shows how a black hole would look like: A black circle that acts as a gravitational lens for light rays coming from behind. How would a rotating black hole look like? How ...
1
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0answers
203 views

Boyer–Lindquist coordinates

In the Kerr solution to the vacuum Einstein Equation written in Boyer–Lindquist coordinates. Because it is not spherical polar coordinates, $r$ ranges from 0 to infinity does not cover all the space, ...
0
votes
0answers
35 views

Help needed to understand Kerr coordinate transformation

The (uncharged) Kerr metric for a black hole of mass $M$ and angular momentum $Ma$ takes the form $$ds^{2} = \Sigma\Big(\frac{dr^{2}}{\Delta} + d\theta^{2}\Big) + (r^{2} + a^{2})\text{sin}^{2}\theta ...
0
votes
0answers
31 views

Easy unit conversion in Kerr metric

I would like to use Kerr metric in Boyer-Lindquist coordinates in geometrized units with mass of the black hole normalized to $M=1$. I am embarrassed to admit, but I can't seem to figure out how to ...
0
votes
0answers
44 views

Cauchy-horizon (Kerr solution)

The Cauchy horizon, particularly the infinite blue shift and why the horizon becomes singular if a object passes him is not really understandable for me. Can anybody explain this mathematically ...