Myers-Perry black holes with scalar hair and a mass gap

TL;DR

This paper constructs five-dimensional rotating black holes with scalar hair that cannot be reduced to known Myers-Perry solutions, revealing a mass gap and emphasizing their inherently non-linear nature unlike Kerr black holes with scalar hair.

Contribution

It introduces a new family of five-dimensional rotating black holes with scalar hair, demonstrating a finite mass gap and their non-linear deviation from Myers-Perry black holes.

Findings

Existence of rotating black holes with scalar hair in five dimensions.

Presence of a finite mass gap between hairy black holes and Myers-Perry black holes.

Scalar hair remains intrinsically non-linear, unlike Kerr black holes with scalar clouds.

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 $J_1=J_2\equiv J$ 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~\cite{Herdeiro:2014goa}. 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.