Back reaction on a Reissner-Nordström black hole

The perturbed (“dressed”) metric of the conformally invariant scalar field in a Reissner-Nordström (RN) black hole is given by solving the semiclassical Einstein and Maxwell equations according to York’s back-reaction approach. Some properties of the “dressed” black hole are obtained, such as its “dressed” mass, the location of the event horizon, and its surface gravity. It will also be found that the hypersurfaces of $r_{+}$ and $r_{-},$ which are the event and Cauchy horizons in the “naked” RN black hole, become spacelike in the perturbed geometry.