Quantum effects in near-extremal charged black hole spacetimes

TL;DR

This paper analytically computes quantum field fluxes near the horizons of near-extremal charged black holes, revealing that quantum effects can drive the black hole interior away from extremality, with results supported by numerical checks.

Contribution

It provides explicit analytical expressions for quantum fluxes at horizons of near-extremal Reissner-Nordström black holes and demonstrates their impact on black hole interior dynamics.

Findings

Quantum effects drive the black hole interior away from extremality.

Analytical expressions for fluxes at horizons are derived.

Numerical checks confirm the analytical results.

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].