  The phenomenon of quantum vacuum polarization in the presence of a
gravitational field is well understood and is expected to have a physical
reality, but studies of its back-reaction on the dynamics of spacetime are
practically non-existent outside the specific context of homogeneous
cosmologies. Building on previous results of quantum field theory in curved
spacetimes, in this letter we first derive the semiclassical equations of
stellar equilibrium in the s-wave Polyakov approximation. It is highlighted
that incorporating the polarization of the quantum vacuum leads to a
generalization of the classical Tolman-Oppenheimer-Volkoff equation. Despite
the complexity of the resulting field equations, it is possible to find exact
solutions. Aside from being the first known exact solutions that describe
relativistic stars including the non-perturbative backreaction of semiclassical
effects, these are identified as a non-trivial combination of the black star
and gravastar proposals.
