Geometrically Regular Black Holes with Hedgehog Scalar Hair

TL;DR

This paper introduces a new class of regular black hole solutions with scalar hair in a modified gravity theory, featuring a de Sitter core and unique thermodynamic properties.

Contribution

It presents exact, asymptotically flat black hole solutions with scalar hair and regular centers, expanding understanding of black hole geometries in scalar-tensor theories.

Findings

Solutions have a de Sitter core and approach Schwarzschild at large distances.

Black holes carry topological scalar hair but no scalar charge.

Curvature invariants remain finite, ensuring geometric regularity.

Abstract

We study a simple theory based on general relativity, minimally coupled to a constrained scalar triplet and to an auxiliary non-propagating three-form sector. Within a spherically symmetric hedgehog ansatz, the theory admits a continuous exact family of asymptotically flat geometrically regular black holes. For a simple choice of kinetic function, the solutions possess a de Sitter core and approach Schwarzschild with the first correction appearing only at order $r^{-4}$. We analyse their horizon structure, thermodynamics, and main strong-field properties. The black holes carry topological scalar hair and a continuous secondary parameter, but no scalar charge. The regularity established here is geometric: the curvature invariants remain finite, although the matter sector is not completely smooth at the centre.