Hunting for fermionic instabilities in charged AdS black holes

27 Apr 2020  ·  Dias Oscar J. C., Masachs Ramon, Papadoulaki Olga, Rodgers Paul ·

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.

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High Energy Physics - Theory General Relativity and Quantum Cosmology