Quantum effects in near-extremal charged black hole spacetimes

Abstract

We compute the semiclassical current and stress-energy fluxes both at the event and Cauchy horizon of a near-extremal Reissner-Nordstr\"om black hole. We consider a minimally-coupled, massless, charged scalar field in the Unruh state, describing an evaporating black hole. The near-extremal domain allows for an analytical treatment of the scattering problem of the Boulware modes both in the interior and exterior regions. We present this and explicit analytical expressions for $\langle j_v\rangle $, $\langle T_{vv}\rangle$ at the horizons, as well as estimates for $\langle j_u\rangle$ and $\langle T_{uu}\rangle $. We cross-check the analytical results numerically by bringing the radial Klein-Gordon equation into the form of the confluent Heun equation. Inserting these expectation values as sources to the Einstein-Maxwell equations, we find that at least in the near-extremal regime of small field charge, quantum effects drive the black hole interior away from extremality. Our work generalizes the known results for the real scalar field [Phys. Rev. D 104, 024066] and is in agreement with recent work on charged fields in expanding Reissner-Nordstr\"om deSitter universes [Phys. Rev. Lett. 127, 231301, Phys. Rev. D 104, 025009].