A classification of admissible energy density profiles with bounded Kretschmann scalar yields a unified framework for regular static spherically symmetric spacetimes satisfying the weak energy condition, recovering known models and producing new families with hypergeometric and other closed forms.
Geometrically Regular Black Holes with Hedgehog Scalar Hair
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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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Analytical black hole solutions are constructed in Einstein-Maxwell-Yang-Mills theory with conformally coupled scalars, generalizing MTZ and AC solutions by including non-Abelian gauge fields determined by horizon curvature.
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Families of regular spacetimes and energy conditions
A classification of admissible energy density profiles with bounded Kretschmann scalar yields a unified framework for regular static spherically symmetric spacetimes satisfying the weak energy condition, recovering known models and producing new families with hypergeometric and other closed forms.
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(Super-)renormalizable hairy meronic black holes
Analytical black hole solutions are constructed in Einstein-Maxwell-Yang-Mills theory with conformally coupled scalars, generalizing MTZ and AC solutions by including non-Abelian gauge fields determined by horizon curvature.