Solutions of the massive Dirac equation in the near-horizon metric of the extremal five dimensional Myers-Perry black hole with equal angular momenta

TL;DR

This paper analytically solves the massive Dirac equation in the near-horizon geometry of an extremal five-dimensional Myers-Perry black hole with equal angular momenta, revealing the angular quantum numbers and radial behavior of fermionic fields.

Contribution

It provides a complete analytical solution to the Dirac equation in this specific black hole background, including angular quantum numbers and radial solutions.

Findings

Angular quantum numbers are determined algebraically.

Radial solutions are expressed in terms of special functions.

Analysis of the near-horizon radial current of the Dirac field.

Abstract

We study massive Dirac fields in the background of the near-horizon limit of the extremal Myers-Perry black hole in five dimensions. We consider the case in which both angular momenta have equal magnitude. The resulting Dirac equation can be decoupled into an angular and a radial part. The solution of the angular part results in some algebraic relations that determine completely the angular quantum numbers of the fermionic field. The radial part can be analytically solved in terms of special functions, which allow us to analyze the near-horizon radial current of the Dirac field.