We investigate the spin-1/2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG, where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.
J. H. Noble and U. D. Jentschura, "Dirac Hamiltonian and Reissner-Nordström metric: Coulomb Interaction in Curved Space-Time," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 93, no. 3, pp. 032108-1-032108-10, American Physical Society (APS), Mar 2016.
The definitive version is available at https://doi.org/10.1103/PhysRevA.93.032108
Keywords and Phrases
Electrostatics; Gravitation; Hamiltonians; Quantum Theory; Spin Dynamics; Electromagnetic Interactions; Electrostatic Coupling; Fine Structure Constants; Foldy-Wouthuysen Transformations; Radially Symmetric; Schwarzschild Geometry; Space Time Geometry; Spin-orbit Couplings; Geometry
International Standard Serial Number (ISSN)
Article - Journal
© 2016 American Physical Society (APS), All rights reserved.
01 Mar 2016