Abstract
We construct a new family of rotating black holes with scalar hair and a regular horizon of spherical topology, within five dimensional (d = 5) Einstein’s gravity minimally coupled to a complex, massive scalar field doublet. These solutions represent generalizations of the Kaluza-Klein monopole found by Gross, Perry and Sorkin, with a twisted S1 bundle over a four dimensional Minkowski spacetime being approached in the far field. The black holes are described by their mass, angular momentum, tension and a conserved Noether charge measuring the hairiness of the configurations. They are supported by rotation and have no static limit, while for vanishing horizon size, they reduce to boson stars. When performing a Kaluza-Klein reduction, the d = 5 solutions yield a family of d = 4 spherically symmetric dyonic black holes with gauged scalar hair. This provides a link between two seemingly unrelated mechanisms to endow a black hole with scalar hair: the d = 5 synchronization condition between the scalar field frequency and the event horizon angular velocity results in the d = 4 resonance condition between the scalar field frequency and the electrostatic chemical potential.
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Acknowledgments
C.H., J.N. and E.R. would like to express their gratitude to Juan Carlos Degollado for being an exceptional host during a visit at the Instituto de Ciencias Físicas, UNAM — Campus de Morelos, Mexico, where a part of this project has been developed. This work is supported by the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT – Fundação para a Ciência e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020. The authors acknowledge support from the projects PTDC/FIS-AST/3041/2020, as well as CERN/FIS-PAR/0024/2021 and 2022.04560.PTDC. This work has further been supported by the European Union’s Horizon 2020 research and innovation (RISE) programme H2020-MSCA-RISE-2017 Grant No. FunFiCO-777740 and by the European Horizon Europe staff exchange (SE) programme HORIZON-MSCA-2021-SE-01 Grant No. NewFunFiCO-101086251. J. N. is supported by the FCT grant 2021.06539.BD.
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Brihaye, Y., Herdeiro, C., Novo, J. et al. Kaluza-Klein monopole with scalar hair. J. High Energ. Phys. 2024, 181 (2024). https://doi.org/10.1007/JHEP01(2024)181
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DOI: https://doi.org/10.1007/JHEP01(2024)181