Regular black holes inspired by quasitopological gravity

Recently it was demonstrated that by adding to the Einstein-Hilbert action a series in powers of the curvature invariants with specially chosen coefficients one can obtain a theory of gravity which has spherically symmetric solutions describing regular black holes. Its reduced action depends on a function of one of the basic curvature invariants of the corresponding metric. In this paper we study a generalization of this model to the case when this function depends on all the basic curvature invariants. We show that the metrics which are solutions of such a model possess a universal scaling property. We demonstrate that there exists a special class of such models for which the ``master'' equation for a basic curvature invariant is a linear second-order ordinary differential equation. We specify a domain in the space of parameters of the model for which the corresponding solutions describe regular static, spherically symmetric black holes and study their properties.