Atomic systems with bound states of fermions in the Schwarzschild, Reissner-Nordstr\"{o}m fields as candidates for the role of dark matters particles

TL;DR

This paper demonstrates the existence of bound fermion states near black hole horizons in Schwarzschild and Reissner-Nordström fields, proposing neutral fermionic systems as potential dark matter candidates.

Contribution

It introduces a relativistic Schrödinger-type equation for fermions in these fields and proves the existence of localized bound states near the event horizon.

Findings

Bound states are localized near the event horizon within a few Compton wavelengths.

Neutral fermionic systems in these fields could serve as dark matter particles.

Stationary states with real, square-integrable wave functions are established.

Abstract

After transition from the Dirac equation to the Schr\"{o}dinger-type relativistic equation with effective potentials of the Schwarzschild and Reissner-Nordstr\"{o}m (RN) fields, the existence of the stationary state of fermions with real square-integrable radial wave functions is proved. The fermions are localized near the event horizon within the range from zero to several fractions or a few units of the Compton wavelength of a fermion as a function of the gravitational and electromagnetic coupling constants and the angular and orbital momenta j,l. Electrically neutral atomic-type systems (Schwarzschild and RN collapsars with fermions in bound states) are proposed as particles of dark matter.