  In the present work we show that, in the linear regime, gravity theories with
more than four derivatives can have remarkable regularity properties if
compared to their fourth-order counterparts. To this end, we derive the
expressions for the metric potentials associated to a pointlike mass in a
general higher-order gravity model in the Newtonian limit. It is shown that any
polynomial model with at least six derivatives in both spin-2 and spin-0
sectors has regular curvature invariants. We also discuss the dynamical problem
of the collapse of a small mass, considered as a spherical superposition of
nonspinning gyratons. Similarly to the static case, for models with more than
four derivatives the Kretschmann invariant is regular during the collapse of a
thick null shell. We also verify the existence of the mass gap for the
formation of mini black holes even if complex and/or degenerate poles are
allowed, generalizing previous considerations on the subject and covering the
case of Lee-Wick gravity. These interesting regularity properties of sixth- and
higher-derivative models at the linear level reinforce the question of whether
there can be nonsingular black holes in the full nonlinear model.
