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

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 timelike 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 the 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 a difference in the corresponding spacetime metrices the resulting complexity arose in separation in the earlier case.