A no-short scalar hair theorem for rotating Kerr black holes. (3rd May 2016)

• Record Type: Journal Article
• Authors: Hod, Shahar
• Is Part Of: Classical and quantum gravity. Volume 33:Number 11(2016:Jun.)
• Publication Date: 2016-05-03
• Subjects: black holes -- scalar fields -- null circular geodesics; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/0264-9381/33/11/114001
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: If a black hole has hair, how short can this hair be? A partial answer to this intriguing question was recently provided by the 'no-short hair' theorem which asserts that the external fields of a spherically symmetric electrically neutral hairy black-hole configuration must extend beyond the null circular geodesic which characterizes the corresponding black-hole spacetime. One naturally wonders whether the no-short hair inequality r hair > r null is a generic property of all electrically neutral hairy black-hole spacetimes. In this paper we provide evidence that the answer to this interesting question may be positive. In particular, we prove that the recently discovered cloudy Kerr black-hole spacetimes—non-spherically symmetric non-static black holes which support linearized massive scalar fields in their exterior regions—also respect this no-short hair lower bound. Specifically, we analytically derive the lower bound r field / r + > r + / r − on the effective lengths of the external bound-state massive scalar clouds (here r field is the peak location of the stationary bound-state scalar fields and r ± are the horizon radii of the black hole). Remarkably, this lower bound is universal in the sense that it is independent of the physical parameters (proper mass and angular harmonic indices) of the exterior scalar fields. Our results suggest that the lower bound r hair > r null may be a general property of asymptotically flat electrically neutral hairy black-hole configurations.