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–Nordstrm spacetime. The complete set of solutions of the semiclassical self-consistent equations is obtained and compared with their classical counterparts. The semiclassical Reissner–Nordstrm 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.

我们在经典的 Reissner-Nordstrm 时空计算正则化 Polyakov 近似中无质量最小耦合标量场的重整化应力-能量张量 (RSET) 及其反向反应。得到了半经典自洽方程组的完整解，并与它们的经典对应方程进行了比较。半经典的 Reissner-Nordstrm 族涉及三种几何形状，它们取决于时空的荷质比。在电荷不足的情况下，几何体的外部视界被虫洞颈取代，虫洞颈在有限的适当距离处导致奇异的渐近区域。过度充电的区域揭示了一个裸奇点，周围环绕着来自量子化场的（无限）质量云。在这两种行为之间，存在一个让人联想到极值黑洞经典几何的分线解。由于极值视界上的 RSET 是有限的，因此半经典反向反应不会摆脱视界。尽管如此，我们证明了由此产生的视界是奇异的。