Electrically charged black hole solutions in semiclassical gravity and dynamics of linear perturbations

Abstract

We explore quantum corrections of electrically charged black holes subject to vacuum polarization effects of fermion fields in QED. Solving this problem exactly is challenging so we restrict to perturbative corrections that one can obtain using the heat kernel expansion in the one-loop effective action for electrons. Starting from the corrections originally computed by Drummond and Hathrell, we solve the full semiclassical Einstein-Maxwell system of coupled equations to leading order in Planck's constant, and find a new electrically charged, static black hole solution. To probe these quantum corrections, we study electromagnetic and gravitational (axial) perturbations on this background, and derive the coupled system of Regge-Wheeler master equations that govern the propagation of these waves. In the classical limit our results agree with previous findings in the literature. We finally compare these results with those that one can obtain by working out the Euler-Heisenberg effective action. We find again a new electrically charged static black hole spacetime, and derive the coupled system of Regge-Wheeler equations governing the propagation of axial electromagnetic and gravitational perturbations. Results are qualitatively similar in both cases. We briefly discuss some challenges found in the numerical computation of the quasinormal mode frequency spectra when quantum corrections are included.