Hunting for fermionic instabilities in charged AdS black holes

TL;DR

This paper investigates whether charged AdS black holes are unstable to fermionic perturbations, finding no linear mode instabilities despite fermions violating near-horizon stability bounds, contrasting with scalar field instabilities.

Contribution

The study demonstrates that Dirac fields do not induce linear instabilities in charged AdS black holes, even when violating near-horizon stability bounds, contrasting with scalar field behavior.

Findings

No fermionic linear mode instabilities found.

Fermions violate near-horizon stability bounds without causing instability.

Scalar fields trigger known near-horizon instabilities.

Abstract

Fermions scattering on a black hole background cannot develop an instability sourced by superradiance. However, in a global (or planar) AdS$_4$-Reissner-Nordstr\"om background fermions can violate the AdS$_2$ fermionic mass stability bound as measured by a near horizon observer at zero temperature. This suggests that AdS-Reissner-Nordstr\"om black holes might still be unstable to Dirac perturbations. Motivated by this observation we search for linear mode instabilities of Dirac fields in these backgrounds but find none. This is in contrast with the scalar field case, where a violation of the near-horizon Breitenl\"ohner-Freedman stability bound in the AdS-Reissner-Nordstr\"om background triggers the already known scalar condensation near-horizon linear instability (in the planar limit this is Gubser's instability that initiated the holographic superconductor programme). We consider both the standard and alternative AdS/CFT quantizations (that preserve the conformal invariance of AdS). These are reflective boundary conditions that have vanishing energy flux at the asymptotic boundary.