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It is shown that polynomial gravity theories with more than four derivativesin each scalar and tensor sectors have a regular weak-field limit, withoutcurvature singularities. This is achieved by proving that in these models theeffect of the higher derivatives can be regarded as a complete regularizationof the delta-source. We also show how this result implies that a wide class ofnon-local ghost-free gravities have a regular Newtonian limit too, and discussthe applicability of this approach to the case of weakly non-local models.

Effective delta sources and regularity in higher-derivative and ghost-free gravity