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 .