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In this paper we will show all the linearized curvature tensors in theinfinite derivative ghost and singularity free theory of gravity in the staticlimit. We have found that in the region of non-locality, in the ultravioletregime (at short distance from the source), the Ricci tensor and the Ricciscalar are not vanishing, meaning that we do not have a vacuum solution anymoredue to the smearing of the source induced by the presence of non-localgravitational interactions. It also follows that, unlike in Einstein's gravity,the Riemann tensor is not traceless and it does not coincide with the Weyltensor. Secondly, these curvatures are regularized at short distances such thatthey are singularity-free, in particular the same happens for the Kretschmanninvariant. Unlike the others, the Weyl tensor vanishes at short distances,implying that the spacetime metric becomes conformally flat in the region ofnon-locality, in the ultraviolet. As a consequence, the non-local region can beapproximated by a conformally flat manifold with non-negative constantcurvatures. We briefly discuss the solution in the non-linear regime, and arguethat $1/r$ metric potential cannot be the solution where non-locality isimportant in the ultraviolet regime.

Classical properties of non-local, ghost- and singularity-free gravity