  In this Letter we derive the gravity field equations by varying the action
for an ultraviolet complete quantum gravity. Then we consider the case of a
static source term and we determine an exact black hole solution. As a result
we find a regular spacetime geometry: in place of the conventional curvature
singularity extreme energy fluctuations of the gravitational field at small
length scales provide an effective cosmological constant in a region locally
described in terms of a de Sitter space. We show that the new metric coincides
with the noncommutative geometry inspired Schwarzschild black hole. Indeed, we
show that the ultraviolet complete quantum gravity, generated by ordinary
matter is the dual theory of ordinary Einstein gravity coupled to a
noncommutative smeared matter. In other words we obtain further insights about
that quantum gravity mechanism which improves Einstein gravity in the vicinity
of curvature singularities. This corroborates all the existing literature in
the physics and phenomenology of noncommutative black holes.
