Reissner-Nordstr\"om geometry counterpart in semiclassical gravity

TL;DR

This paper analyzes the effects of quantum fields on Reissner-Nordstr"om black holes, revealing that quantum backreaction can significantly alter the classical geometry, leading to wormholes, naked singularities, or extremal horizons with singular features.

Contribution

It provides the first comprehensive semiclassical analysis of Reissner-Nordstr"om spacetime, including solutions with quantum backreaction and their geometric implications.

Findings

Under-charged regime forms wormholes instead of horizons.

Over-charged regime results in naked singularities with quantum matter.

Extremal horizons remain but become singular under quantum effects.

Abstract

We compute the Renormalized Stress-Energy Tensor (RSET) of a massless minimally coupled scalar field in the Regularized Polyakov approximation, as well as its backreaction, on the classical Reissner-Nordstr\"om spacetime. The complete set of solutions of the semiclassical self-consistent equations is obtained and compared with the classical counterparts. The semiclassical Reissner-Nordstr\"om family involves three kinds of geometries that depend on the charge-to-mass ratio of the spacetime. In the under-charged regime, the geometry has its external horizon replaced by a wormhole neck that leads to a singular asymptotic region at finite proper distance. The over-charged regime reveals a naked singularity coated by a cloud of (infinite) mass coming from the quantized field. In between both behaviours there is a separatrix solution reminiscent of the extremal black hole classical geometry. As the RSET over an extremal horizon is finite, the semiclassical backreaction does not get rid of the horizon. Nonetheless, we show that the resulting horizon is singular.