  We present strong evidence that semiclassical gravity can give place to
self-consistent ultracompact stars beyond the Buchdahl limit. We integrate the
semiclassical equations of (spherically symmetric) stellar equilibrium for a
constant-density classical fluid. The semiclassical contribution is modelled by
a quantum massless scalar field in the only static vacuum state compatible with
asymptotic flatness (Boulware vacuum). The Renormalized Stress-Energy Tensor
(RSET) is firstly approximated by the analytic Polyakov approximation. This
already reveals a crucial difference with respect to purely classical
solutions: stars with compactness close to that of a black hole exhibit bounded
pressures and curvatures up to a very small central core compared with the star
radius. This suggests that a more refined approximation to the RSET at the core
may give rise to strictly regular configurations. Following this suggestion, we
prove that a minimal deformation of the Polyakov approximation inside the
central core is sufficient to produce regular ultracompact stellar
configurations.
