Separation of Dirac equation in the 3+1 dimensional constant curvature black hole background and its solution

TL;DR

This paper investigates the Dirac equation in a 3+1-dimensional constant curvature black hole spacetime, demonstrating its separability with a specific basis and analyzing differences from the Kerr black hole case.

Contribution

It presents a method to separate and solve the Dirac equation in CCBH spacetime, highlighting differences from Kerr geometry due to metric variations.

Findings

Successfully separated the Dirac equation in CCBH spacetime

Obtained explicit solutions for spin-half particles

Identified structural differences from Kerr black hole equations

Abstract

The behavior of spin-half particles is discussed in the 3 + 1-dimensional constant curvature black hole (CCBH) spacetime. We use Schwarzschild-like coordinates, valid outside the black hole event horizon. The constant time surfaces corresponding to the time-like Killing vector are degenerate at the black hole event horizon and also along an axis. We write down the Dirac equation in this spacetime using Newman-Penrose formalism which is not easily separable unlike that in the Kerr metric. However, with a particular choice of basis system the equation is separable and we obtain the solutions. We discuss the structural difference in the Dirac equation in the CCBH spacetime with that in the Kerr geometry, due to difference in the corresponding spacetime metric, resulting complexity arised in separation in the earlier case.