Finite motion of electrons in the field of microscopic black holes

Abstract

In the single-particle approximation of the Dirac equation, a study is made of the finite motion of electrons in the field of small black holes (M ≪< 1017 g) under the assumption that the black hole has rotation (a ≪< M) and charge much less than the critical value (Z < 137). In this case, the motion of the particle is nonrelativistic, and the energy spectrum is hydrogen-like. The influence of rotation of the hole on the binding energy of the particle is small and unimportant for determining the damping of the levels due to capture by the hole. In contrast to a scalar particle, the damping of the electron states is not replaced by excitation for ω < mjΩH + eVH. The gravitational spin-orbit interaction has a strong influence on the damping. The probability of capture of an electron with spin anti-parallel to the orbital angular momentum is much greater than the probability of capture for a particle with spin parallel to it. In the Schwarzschild field, the damping of the S state of an electron is eight times less than the damping of the ground state of a scalar particle.