Weak-field limit and regular solutions in polynomial higher-derivative gravities

TL;DR

This paper demonstrates that higher-derivative gravity theories with more than four derivatives exhibit remarkable regularity in the linear regime, potentially leading to nonsingular black hole solutions.

Contribution

It derives metric potentials in polynomial higher-derivative gravity models and shows regularity of curvature invariants during collapse, extending previous results to more general models.

Findings

Higher-derivative models with at least six derivatives have regular curvature invariants.

The Kretschmann invariant remains regular during collapse in these models.

A mass gap exists for mini black hole formation, even with complex poles.

Abstract

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.