  In this paper we will show all the linearized curvature tensors in the
infinite derivative ghost and singularity free theory of gravity in the static
limit. We have found that in the region of non-locality, in the ultraviolet
regime (at short distance from the source), the Ricci tensor and the Ricci
scalar are not vanishing, meaning that we do not have a vacuum solution anymore
due to the smearing of the source induced by the presence of non-local
gravitational interactions. It also follows that, unlike in Einstein's gravity,
the Riemann tensor is not traceless and it does not coincide with the Weyl
tensor. Secondly, these curvatures are regularized at short distances such that
they are singularity-free, in particular the same happens for the Kretschmann
invariant. Unlike the others, the Weyl tensor vanishes at short distances,
implying that the spacetime metric becomes conformally flat in the region of
non-locality, in the ultraviolet. As a consequence, the non-local region can be
approximated by a conformally flat manifold with non-negative constant
curvatures. We briefly discuss the solution in the non-linear regime, and argue
that $1/r$ metric potential cannot be the solution where non-locality is
important in the ultraviolet regime.
