Motion of half-spin particles in the axially symmetric field of naked singularities of 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). The analysis was performed by means of the method of effective potentials of the Dirac equation generalized for the case when radial and angular variables are not separated. As $-1<q<q_{lim},|q_{lim}|<<1$ the naked singularities do not except the existence of stationary bound states of Dirac particles for a prolate mass distribution in the q-metric along the axial axis. For the oblate mass distribution, the naked singularities of the q-metric are separated from the Dirac particle by infinitely large repulsive barriers with the subsequent potential well deepening while moving along the angle from the equator (or from $\theta ={\theta }_{min},\theta =\pi -{\theta }_{min}$) towards poles. The exception are the poles and, as $0<q<q\ast$, some points ${\theta }_i$ for the states of the particle with j>=3/2.

22 pages, 5 figures, 2 tables

References in corpus (3)

• Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities
• Uniqueness and Self-Conjugacy of Dirac Hamiltonians in arbitrary Gravitational Fields
• Solution of the problem of uniqueness and hermiticity of hamiltonians for Dirac particles in gravitational fields

Cited by in corpus (2)

• Quantum mechanics of stationary states of particles in a space-time of classical black holes
• The space-time line element for static ellipsoidal objects