ON QUASILEVELS IN THE GRAVITATIONAL-FIELD OF A BLACK-HOLE

Quantum tunnelling of scalar particles with energies near the top of an effective potential barrier which corresponds to a circular classically unstable orbit is investigated. The corresponding lifetime has a rather smooth logarithmic dependence on the parameters of the problem. For the Kerr metric the lifetime of a particle counter-rotating with respect to a black hole along a circular orbit is shown to depend weakly on the hole angular momentum whereas in the co-rotating case it increases significantly for a rapidly rotating black hole.