1.1 Gravitational capture of non-relativistic particles

We now consider the gravitational capture of particles by a rotating black hole. The impact parameter b_⊥ of capturing a nonrelativistic particle moving in the equatorial plane is given by the expression:

 (1.1)

The capture cross section for particles falling perpendicularly to the rotation axis of the black hole with a = M

 (1.2)

The impact parameter of particles falling parallel to the rotation axis, b_||, can be found in the following manner. Let us denote ˜b_|| = b_||/M, ˜a = a/M. Then ˜b_|| is found as the solution of the equation

 (1.3)

where . If ˜a = 1, then

 (1.4)

1.2 Gravitational capture of ultrarelativistic particles

Consider now ultrarelativistic particles. The impact parameters of capture, b_⊥, for the motion in the equatorial plane are given by the following formulas.

If the angular momentum is positive, then

 (1.5)

If the angular momentum is negative, then

 (1.6)

In this case the cross section for ˜a = 1 is

 (1.7)

For photons propagating parallel to the rotation axis of the black hole with ˜a = 1, we have

 (1.8)

A rotating black hole captures incident particles with a lower efficiency than a non-rotating black hole of the same mass does.