Reissner–Nordström geometry counterpart in semiclassical gravity

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–Nordström spacetime. The complete set of solutions of the semiclassical self-consistent equations is obtained and compared with their classical counterparts. The semiclassical Reissner–Nordström family involves three kinds of geometries that arise depending 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 surrounded by a cloud of (infinite) mass coming from the quantized field. 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.