Quantum mechanics of stationary states of particles in external singular spherically and axially symmetric gravitational and electromagnetic fields

The report considers the interaction of scalar particles, photons and fermions with the gravitational and electromagnetic Schwarzschild, Reissner-Nordstr\"{o}m, Kerr and Kerr-Newman fields. The behavior of effective potentials in the relativistic Schr\"{o}dinger-type second-order equations is analyzed. It was found that the quantum theory is incompatible with the hypothesis of the existence of classical black holes with event horizons of zero thickness that were predicted based on solutions of the general relativity (GR) with zero and non-zero cosmological constant \(\Lambda\). The alternative may be presented by compound systems, i.e., collapsars with fermions in stationary bound states.