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-Nordström black hole. We consider a minimally coupled, massless, weakly 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 ⟨jv⟩ and ⟨Tvv⟩ at the horizons, as well as estimates for ⟨ju⟩ and ⟨Tuu⟩. 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 [Noa Zilberman and Amos Ori, Quantum fluxes at the inner horizon of a near-extremal spherical charged black hole, .] and is in agreement with recent work on charged fields in expanding Reissner–Nordström–de Sitter universes [Christiane Klein , Quantum (dis)charge of black hole interiors, ., Christiane Klein and Jochen Zahn, Renormalized charged scalar current in the Reissner–Nordström–de Sitter spacetime, .]. Published by the American Physical Society 2025