  We investigate the effects of vacuum polarization on vacuum static
spherically-symmetric spacetimes. We start from the Polyakov approximation to
the renormalized stress-energy tensor (RSET) of a minimally coupled massless
scalar field. This RSET is not regular at $r=0$, so we define a regularized
version of the Polyakov RSET. Using this Regularized RSET, and under the
previous symmetry assumptions, we find all the solutions to the semiclassical
field equations in vacuum. The resulting counterpart to the Schwarzschild
classical geometry substitutes the presence of an event horizon by a wormhole
throat that connects an external asymptotically flat region with an internal
asymptotic region possessing a naked singularity: there are no semiclassical
vacuum solutions with well-defined Cauchy surfaces. We also show that the
Regularized Polyakov RSET allows for wormhole geometries of arbitrarily small
throat radius. This analysis paves the way to future investigations of proper
stellar configurations with an internal non-vacuum region.
