Abstract
This contribution reviews the recent discovery of a certain class of—regular on and outside the horizon—exact hairy black hole solutions in four dimensional general relativity. Their construction follows from the integrability of a cohomogeneity two Weyl rescaling of the Carter–Debever ansatz in the presence of an arbitrary number of scalar fields with an arbitrary self interaction and an arbitrary non-minimal coupling to the scalar curvature. Two field equations, independent of the specific form of the energy momentum tensor, are used to integrate the metric. The remaining ones fix the form of the scalar field self interaction. The cohomogeneity one black holes are described and are shown to encompass all the exact—regular in the domain of outer communications—uncharged, black holes with a minimally coupled scalar hair, available in the literature.
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Acknowledgments
The author would like to thank the organizers of the conference “ Relativity and Gravitation—100 years after Einstein in Prague” for its excellent environment and organization. Research of Andrés Anabalón is supported in part by the Conicyt grant Anillo ACT-91: “Southern Theoretical Physics Laboratory” (STPLab) and by the FONDECYT grant 11121187.
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Anabalón, A. (2014). Exact Hairy Black Holes. In: Bičák, J., Ledvinka, T. (eds) Relativity and Gravitation. Springer Proceedings in Physics, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-06761-2_1
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