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

TL;DR

This paper solves the Dirac equation in rotating Bertotti-Robinson spacetime, providing exact solutions for the axial part and analytical or numerical approaches for the angular part depending on particle mass.

Contribution

It presents the first exact solutions for the Dirac equation in this spacetime and analyzes both massless and massive cases using special functions and numerical methods.

Findings

Axial equation solved exactly using hypergeometric functions.

Angular equation for neutrinos solved with confluent Heun functions.

Massive case requires numerical methods for angular solutions.

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 angular part. The axial equation, which is independent of mass, is solved exactly in terms of hypergeometric functions. The angular equation is considered both for massless (neutrino) and massive spin-(1/2) 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 numerical study.