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arXiv · 2602.16773

Regular black holes from pure gravity in four dimensions

Johanna Borissova·Raúl Carballo-Rubio
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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.

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Johanna Borissova, Raúl Carballo-Rubio. 2026-02-18. Regular black holes from pure gravity in four dimensions. https://doi.org/10.1103/6x2z-qbkh

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