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Physical Review D

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Ergosurfaces for Kerr black holes with scalar hair

Carlos Herdeiro^* and Eugen Radu^†

Departamento de Física da Universidade de Aveiro and I3N Campus de Santiago, 3810-183 Aveiro, Portugal

^*herdeiro@ua.pt
^†eugen.radu@ua.pt

Phys. Rev. D 89, 124018 – Published 13 June, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.124018

Abstract

We have recently reported the existence of Kerr black holes with scalar hair in General Relativity minimally coupled to a massive, complex scalar field [C. Herdeiro and E. Radu, Phys. Rev. Lett. 112, 221101 (2014)]. These solutions interpolate between boson stars and Kerr black holes. The latter have a well-known topologically $S^{2}$ ergosurface (ergosphere) whereas the former develop a $S^{1} \times S^{1}$ ergosurface (ergotorus) in a region of parameter space. We show that hairy black holes always have an ergoregion, and that this region is delimited by either an ergosphere or an ergo-Saturn—i.e. a $S^{2} \oplus (S^{1} \times S^{1})$ ergosurface. In the phase space of solutions, the ergotorus can either appear disconnected from the ergosphere or pinch off from it. We provide a heuristic argument, based on a measure of the size of the ergoregion, that superradiant instabilities—which are likely to be present—are weaker for hairy black holes than for Kerr black holes with the same global charges. We observe that Saturn-like, and even more remarkable, ergosurfaces should also arise for other rotating “hairy” black holes.

Article Text

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