The Dirac equation in D-dimensional spherically symmetric spacetimes

TL;DR

This paper details a method to reduce the Dirac equation in D-dimensional spherically symmetric spacetimes to simpler equations and applies it to compute quasinormal frequencies in Nariai spacetime.

Contribution

It provides a detailed method for reducing the Dirac equation in higher-dimensional spherically symmetric spacetimes and applies it to find exact quasinormal frequencies.

Findings

Exact calculation of Dirac quasinormal frequencies in D-dimensional Nariai spacetime.

Method simplifies the analysis of Dirac fields in higher-dimensional curved spacetimes.

Demonstrates the applicability of reduction techniques to specific spacetime geometries.

Abstract

We expound in detail a method frequently used to reduce the Dirac equation in D-dimensional (D >= 4) spherically symmetric spacetimes to a pair of coupled partial differential equations in two variables. As a simple application of these results we exactly calculate the quasinormal frequencies of the uncharged Dirac field propagating in the D-dimensional Nariai spacetime.