  With the back reaction of the vacuum energy-momentum tensor consistently
taken into account, we study static spherically symmetric black-hole-like
solutions to the semi-classical Einstein equation. The vacuum energy is assumed
to be given by that of 2-dimensional massless scalar fields, as a widely used
model in the literature for black holes. The solutions have no horizon.
Instead, there is a local minimum in the radius. We consider thin shells as
well as incompressible fluid as the matter content of the black-hole-like
geometry. The geometry has several interesting features due to the back
reaction of vacuum energy. In particular, Buchdahl's inequality can be violated
without divergence in pressure, even if the surface is below the Schwarzschild
radius. At the same time, the surface of the star can not be far below the
Schwarzschild radius for a density not much higher than the Planck scale, and
the proper distance from its surface to the origin can be very short even for
very large Schwarzschild radius. The results also imply that, contrary to the
folklore, in principle the Boulware vacuum can be physical for black holes.
