Hunting for fermionic instabilities in charged AdS black holes

Abstract

Fermions scattering on a black hole background cannot develop an instability sourced by superradiance. However, in a global (or planar) AdS 4-Reissner-Nordström 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-Nordström 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 Breitenlöhner-Freedman stability bound in the AdS-Reissner-Nordström 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.

How to make traversable wormholes: eternal AdS4 wormholes from coupled CFT’s

“…These instabilities can be understood, for near-extremal black holes, as originating from the difference between the Breitenlöhner Freedman bounds for AdS 2 and AdS 4 ; fields that are allowed tachyons in the asymptotic AdS 4 spacetime lead to instabilities in the AdS 2 near-horizon region. Even though intuitively similar arguments would lead to fermionic instabilities, no evidence for the existence of fermionic hairy black holes has been found [46]. Since the argument crucially depends on the fact that there is an asymptotic AdS 2 geometry, we expect the same result to hold for the wormhole phase.…”

How to Make Traversable Wormholes: Eternal AdS$_4$ Wormholes from Coupled CFT's

“…These instabilities can be understood, for near-extremal black holes, as originating from the difference between the Breitenlöhner Freedman bounds for AdS 2 and AdS 4 ; fields that are allowed tachyons in the asymptotic AdS 4 spacetime lead to instabilities in the AdS 2 nearhorizon region. Even though intuitively similar arguments would lead to fermionic instabilities, no evidence for the existence of fermionic hairy black holes has been found [45]. Since the argument crucially depends on the fact that there is an asymptotic AdS 2 geometry, we expect the same result to hold for the wormhole phase.…”

Strong Cosmic Censorship and eigenvalue repulsions for rotating de Sitter black holes in higher-dimensions

“…To validate our matched asymptotic expansion and to simultaneously identify the NH modes, we compare this analytical expression for the frequency with the numerical data. In the literature there are systems where a similar strategy proved to be very useful and successful [4,17,66,67]. The explicit derivation presented here is for N = 1 (for clarity of the presentation), but the approach generalises, and the main result that we present in the end is valid for all N .…”