Regular black holes from pure gravity in four dimensions

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.

34 pages + appendix; published version

References in corpus (2)

• Dust collapse in asymptotic safety: a path to regular black holes
• Regular Vaidya solutions of effective gravitational theories

Cited by in corpus (2)

• Modified Friedmann equations and non-singular cosmologies in $d=4$ non-polynomial quasi-topological gravities
• Regular ultracompact objects with anti-de Sitter cores as polymerized vacuum solutions