Dirac particle in Newman-Unti-Tamburino spacetime

Abstract

We derive the Dirac equation for a particle in the background of the Newman-Unti-Tamburino (NUT) spacetime by applying the tetrad formalism, and separate the angular and radial parts. We get the system of two differential equations for angular functions and the system of four differential equations for radial functions. We solve the angular equations in terms of hypergeometric functions and find the NUT-charge dependent quantization rule for the angular separation constant. As a result of studying the radial equations, we demonstrate that the probability of particle-antiparticle production on the outer event horizon decreases with the increase of the NUT charge. For the massless fermion, we construct the solution of the radial system of Dirac equation in terms of the confluent Heun functions that allows to get the NUT-charge dependent scattering resonances with imaginary energies. Under the assumption of small NUT charge, we study the extremal NUT black hole with a single horizon, when the Bekenstein-Hawking entropy vanishes identically, and reveal the non-zero NUT charge effects in wave characteristics.