Classical stability of black holes under massless Dirac perturbations

TL;DR

This paper investigates the classical stability of black holes under massless Dirac perturbations, simplifying the equations in higher dimensions and applying the S-deformation method to establish stability results.

Contribution

It extends stability analysis to D-dimensional black holes using the S-deformation method, even when effective potentials are not positive definite.

Findings

At least one effective potential is not positive definite outside the horizon.

The S-deformation method can establish classical stability despite non-positive potentials.

Results are extended to maximally symmetric black holes.

Abstract

In a D-dimensional maximally symmetric spacetime we simplify the massless Dirac equation to two decoupled wavelike equations with effective potentials. Furthermore in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes we note that for the massless Dirac field moving in the region exterior to the event horizon at least one of the effective potentials is not positive definite. Therefore the classical stability of these black holes against this field is not guaranteed. Here with the help of the S-deformation method, we state their classical stability against the massless Dirac field, extend these results to maximally symmetric black holes, and comment on the applicability of our results to establish the stability with respect to other classical fields.