Motion of spin-half particles in the axially symmetric field of naked singularities of the static q-metric

Abstract

Quantum-mechanical motion of a half-spin particle was examined in the axially symmetric field of static naked singularities formed by mass distribution with quadrupole moment (q-metric). .

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

“…Indeed, the uniqueness theorem for black holes [59] states that the most general asymptotically flat vacuum solution of the equations of general relativity theory is the Kerr metric with a monopole mass M and the angular momentum J. Any deviation from a spherically symmetric mass distribution leads to the event horizon vanishing and the occurence of several naked singularities in its place (see static and stationary q-metrics in [60] - [62]).…”

Analysis of Half-Spin Particle Motion in Kerr–Newman Field by Means of Effective Potentials in Second-Order Equations

“…In this paper, a self-conjugate Dirac Hamiltonian with a flat scalar product of wave functions was obtained for the Kerr-Newman field. Since this Hamiltonian does not permit separation of angular and radial variables, similarly to [37], we generalized the method of obtaining effective potentials while squaring Dirac equations. As a result, the polar angle  is a parameter in the radial Schrödinger-type equation.…”

“…In [31] - [33], the method of effective potentials was used to analyze the motion of electrons and positrons in the Coulomb field. In [34] - [37], this method was applied to analyze the motion of Dirac particles in the Schwarzschild and Reissner-Nordström gravitational fields and in the field of naked singularities of the static q -metric [38].…”

“…We examine the Kerr-Newman fields with two horizons, the extreme Kerr-Newman fields with a single horizon and Kerr-Newman naked singularities. For such analysis, the self-conjugate Dirac Hamiltonian is obtained, and, as in [37], the method of obtaining effective potentials in the Schrödinger-type equation is generalized to the case where radial and angular variables are not separated.…”