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### 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 ...
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### 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 \...
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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 + r^2(... 1answer 172 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, ... 1answer 63 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 ... 1answer 109 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} &... 0answers 89 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: V(r)=(1-\epsilon)^2r^4-2Mr^... 0answers 46 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 ... 0answers 61 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| (... 0answers 64 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 ... 0answers 99 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 ... 0answers 53 views ### Kerr Metric and Asymptotically Static Frame Suppose we are given a Kerr spacetime (e.g. containing a single uncharged rotating black hole). How does one know that the coordinates chosen is rotating or non-rotating as seen from infinity? And how ... 0answers 58 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 ... 0answers 65 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 ... 0answers 37 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 ... 0answers 31 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 ... 0answers 116 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 ... 0answers 226 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, ... 0answers 36 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 ...
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 ...