Solution of the Dirac equation in the rotating Bertotti–Robinson spacetime

Abstract

The Dirac equation is solved in the rotating Bertotti–Robinson spacetime. The set of equations representing the Dirac equation in the Newman–Penrose formalism is decoupled into an axial and an angular part. The axial equation, which is independent of mass, is exactly solved in terms of hypergeometric functions. The angular equation is considered both for massless (neutrino) and massive spin-12 particles. For the neutrinos, it is shown that the angular equation admits an exact solution in terms of the confluent Heun equation. In the existence of mass, the angular equation does not allow an analytical solution, however, it is expressible as a set of first order differential equations apt for a numerical study.