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 shell of such particles, initially spherical, becomes prolate along the axis of symmetry during the fall onto 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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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 shell of such particles, initially spherical, becomes prolate along
the axis of symmetry during the fall onto 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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The authors investigate the motion of a test particle in the Kerr metric using Boyer-Lindquist coordinates, extending the results of de Felice and Calvani (FC) (1972) to cases not covered by them, and also considering further details concerning, in particular, photons moving along the principal null congruences. Whereas FC considered only nonnegative values of L = q + l-squared, here negative values are treated. Curves are drawn showing l-aquared as a function of Theta for a fixed positive Gamma and typical values of L, demonstrating the oscillatory nature of the latitudinal motion. Four families of photon world lines with constant latitudes are found. A graph of L/a-squared versus x for a fixed l/a is drawn from calculations, which is used to analyze the r-motions of photons.
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