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.



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)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2016 American Physical Society (APS), All rights reserved.

Publication Date

01 Mar 2016

Included in

Physics Commons