https://doi.org/10.1140/epjc/s10052-019-6727-2
Regular Article - Theoretical Physics
Weak-field limit and regular solutions in polynomial higher-derivative gravities
1
Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Urca, Rio de Janeiro, RJ, 22290-180, Brazil
2
Departamento de Física, ICE, Universidade Federal de Juiz de Fora, Juiz de Fora, MG, 36036-330, Brazil
* e-mail: breno@cbpf.br
Received:
3
October
2018
Accepted:
26
February
2019
Published online:
9
March
2019
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 counterpart. 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.
© The Author(s), 2019
