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arXiv · 2604.15758

Geometrically Regular Black Holes with Hedgehog Scalar Hair

Sebastian Bahamonde
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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.

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Sebastian Bahamonde. 2026-04-17. Geometrically Regular Black Holes with Hedgehog Scalar Hair. https://doi.org/10.1103/tl59-my4v

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