Stationary Bound States of Dirac Particles in Collapsar Fields

TL;DR

This paper finds stationary bound states of Dirac particles in a Schwarzschild gravitational field, revealing potential implications for cosmology and black hole physics by analyzing the particles' energy spectrum with specific boundary conditions.

Contribution

It introduces a method to determine discrete energy levels of Dirac particles near collapsars using a self-conjugate Hamiltonian and boundary conditions at the event horizon.

Findings

Discrete energy spectrum for Dirac particles in Schwarzschild field

Boundary condition ensuring zero azimuthal current at the horizon

Implications for cosmological models and collapsar interactions

Abstract

Stationary bound states of elementary spin 1/2 particles that do not decay with time are obtained for a Schwarzschild gravitational field using a self-conjugate Hamiltonian with a flat scalar product at small values of gravitational coupling constant. In order to obtain a discrete energy spectrum, we introduce a boundary condition such that the azimuthal current density of Dirac particles on the "event horizon" is zero. The results can lead to revisiting some concepts of the standard cosmological model related to the evolution of the universe and interaction of collapsars with surrounding matter.