Regular black holes from pure gravity in four dimensions

TL;DR

This paper introduces new purely gravitational theories in four dimensions that produce regular black hole solutions, including the Hayward spacetime, by constructing non-polynomial gravities with second-order equations.

Contribution

It develops non-polynomial quasi-topological gravity theories in four dimensions that yield regular black hole solutions as vacuum solutions.

Findings

Derivation of static spherically symmetric regular black holes from pure gravity.

Explicit construction of gravitational actions for Hayward regular black holes.

Solutions characterized by algebraic equations for the metric function.

Abstract

We derive static spherically symmetric regular black holes as vacuum solutions to purely gravitational theories in four dimensions. To that end, we construct four-dimensional non-polynomial gravities starting from subclasses of two-dimensional Horndeski actions. By construction, these theories possess second-order equations of motion on spherically symmetric backgrounds. We show that a subset of these non-polynomial gravities, referred to as non-polynomial quasi-topological gravities, admit single-function static spherically symmetric solutions whereby the metric function is determined by an algebraic equation. Solutions to these theories include the Hayward regular black-hole spacetime, for which a corresponding gravitational action is stated explicitly.