GRAVITATIONAL-RADIATION FROM AN EXTREME KERR BLACK-HOLE

We analytically investigate gravitational radiation induced by a test particle falling into an extreme Kerr black hole. Assuming the radiation is dominated by the infinite sequence of quasi-normal modes which has the limiting frequency m/(2 M), where m is an azimuthal eigenvalue and M is the mass of the black hole. we find the radiated energy diverges logarithmically in time. Then we evaluate the back reaction to the black hole by appealing to the energy and angular momentum conservation laws. We find the radiation has a tendency to increase the ratio of the angular momentum to mass of the black hole, which is completely different from the non-extreme case, while the contribution of the test particle is to decrease it. © 1990 Plenum Publishing Corporation.