  The inclusion of the quantum fluctuations of the metric in the geometric
action is a promising avenue for the understanding of the quantum properties of
gravity. In this approach the metric is decomposed in the sum of a classical
and of a fluctuating part, of quantum origin, which can be generally expressed
in terms of an arbitrary second order tensor, constructed from the metric, and
from the thermodynamic quantities describing matter fields. In the present
paper we investigate the effects of the quantum fluctuations on the spherically
symmetric static black hole solutions of the modified field equations, obtained
from a variational principle, by assuming that the quantum correction tensor is
given by the coupling of a scalar field to the metric tensor. After
reformulating the field equations in a dimensionless form, and by introducing a
suitable independent radial coordinate, we obtain their solutions numerically.
We detect the formation of a black hole from the presence of a singularity in
the metric tensor components. Several models, corresponding to different
functional forms of the scalar field potential, are considered. The
thermodynamic properties of the black hole solutions (horizon temperature,
specific heat, entropy and evaporation time due to Hawking luminosity) are also
investigated.
