Properties of Kerr Spacetime

Kerr spacetime describes a rotating black hole. The line element in Boyer–Lindquist coordinates is given by
with and . is the mass of the black hole and is the angular momentum.
The roots of the function define the event horizon and the inner horizon , where . The region between the event horizon and the static limit is called the ergosphere.
The two marginally stable timelike circular geodesics are defined by the radii , where and . An object on the smaller radius rotates with the Kerr black hole, whereas an object on the larger radius rotates in the opposite direction.
The direct (-) and retrograde (+) photon orbits are defined via .
Here, the mass of the black hole is taken as .


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A detailed discussion of the parameters is given in:
J. M. Bardeen, W. H. Press, and S. A. Teukolsky, "Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation," The Astrophysical Journal, 178, 1972 pp. 347–369.
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