Abstract
We construct a family of asymptotically flat, rotating black holes with scalar hair and a regular horizon, within five dimensional Einstein's gravity minimally coupled to a complex, massive scalar field doublet. These solutions are supported by rotation and have no static limit. They are described by their mass M, two equal angular momenta J1=J2≡J and a conserved Noether charge Q, measuring the scalar hair. For vanishing horizon size the solutions reduce to five dimensional boson stars. In the limit of vanishing Noether charge density, the scalar field becomes point-wise arbitrarily small and the geometry becomes, locally, arbitrarily close to that of a specific set of Myers–Perry black holes (MPBHs); but there remains a global difference with respect to the latter, manifest in a finite mass gap. Thus, the scalar hair never becomes a linear perturbation of MPBHs. This is a qualitative difference when compared to Kerr black holes with scalar hair [1]. Whereas the existence of the latter can be anticipated in linear theory, from the existence of scalar bound states on the Kerr geometry (i.e. scalar clouds), the hair of these MPBHs is intrinsically non-linear.
Highlights
Introduction and motivationMyers-Perry black holes (MPBHs) [2] have played an important role in exploring higher dimensional gravity
The AdS5 MPBH solutions in [17] have been found for a rather similar metric ansatz and a vanishing scalar potential, U (|Ψ|) = 0; in this case spacetime asymptotics supply the required confining mechanism so that scalar clouds can be found at linear level
Before discussing the MPBHs with scalar hair and a mass gap, it is useful to review the basic properties of the solitonic limit of the solutions
Summary
Myers-Perry black holes (MPBHs) [2] have played an important role in exploring higher dimensional gravity. The different nature of the gravitational interaction in higher dimensions endows MPBHs with a number of qualitatively distinct properties, when compared the Kerr solution One such distinction can already be seen in the zero angular momentum limit, i.e. at the level of the Tangherlini solutions [4]. When the horizon size vanishes, the solutions reduce to a set of the asymptotically flat, d = 5 rotating boson stars found in [18], in complete analogy to the horizonless limit of the Kerr BHs with scalar hair. Unlike the latter, the d = 5 solutions we shall exhibit do not admit a limit of vanishing Noether charge. The higher dimensional shorter range gravity may still produce gravitational trapping; but this requires non-linear effects
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