Regular black holes inspired by quasi-topological gravity

TL;DR

This paper generalizes a class of modified gravity theories that produce regular black hole solutions by allowing the key function to depend on all basic curvature invariants, revealing universal properties and specific solution classes.

Contribution

It extends previous models by considering a function of all curvature invariants, identifying conditions for regular black hole solutions, and analyzing their properties.

Findings

Existence of a universal scaling property for solutions.

Identification of a parameter domain for regular black holes.

Derivation of a linear second order master equation.

Abstract

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.