Semiclassical charged black holes with a quantized massive scalar field

Semiclassical perturbations to the Reissner-Nordström metric caused by the presence of a quantized massive scalar field with arbitrary curvature coupling are found to first order in $\epsilon =ħ{/M}^2.$ The DeWitt-Schwinger approximation is used to determine the vacuum stress-energy tensor of the massive scalar field. When the semiclassical perturbation are taken into account, we find extreme black holes will have a charge-to-mass ratio that exceeds unity, as measured at infinity. The effects of the perturbations on the black hole temperature (surface gravity) are studied in detail, with particular emphasis on near extreme “bare” states that might become precisely zero temperature “dressed” semiclassical black hole states. We find that for minimally or conformally coupled scalar fields there are no zero temperature solutions among the perturbed black holes.