Quantum mechanics of stationary states of particles in a space-time of classical black holes

Abstract

We consider interactions of scalar particles, photons, and fermions in Schwarzschild, Reissner-Nordstr\"om, Kerr, and Kerr-Newman gravitational and electromagnetic fields with a zero and nonzero cosmological constant. We also consider interactions of scalar particles, photons, and fermions with nonextremal rotating charged black holes in a minimal five-dimensional gauge supergravity. We analyze the behavior of effective potentials in second-order relativistic Schr\"odinger-type equations. In all cases, we establish the existence of the regime of particle "falling" on event horizons. An alternative can be collapsars with fermions in stationary bound states without a regime of particles "falling".