The Fall of the Shell of Dust on to a Rotating Black Hole

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Abstract
The motion of particles falling radially from rest at infinity with zero total angular momentum on to a rotating (Kerr) black hole is studied. The motion is examined analytically for large distances as well as near the horizon and also numerically in the case of an extreme Kerr black hole. The shell of such particles, initially spherical, becomes prolate along the axis of symmetry during the fall on to a rotating hole. The shape of the shell from the viewpoint of distant observers is studied by means of the photons moving along the (non-shearing) geodesics of the outgoing principal null congruence. The approach of the particles towards the horizon in terms of the arrival times of these photons to a distant observer, the redshift of the radiation and its intensity show dependence exponentially on the observer's proper time as in the non-rotating case, however the characteristic e-folding times become infinite as the hole's angular momentum approaches the extreme value. In the case of an extreme Kerr black hole these exponential laws go over into power laws.

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