Kerr black holes with self-interacting scalar hair: hairier but not heavier

Carlos A. R. Herdeiro; Eugen Radu; Helgi Rúnarsson

doi:10.1103/PhysRevD.92.084059

paper

Kerr black holes with self-interacting scalar hair: hairier but not heavier

arXiv:1509.02923 · doi:10.1103/PhysRevD.92.084059

Abstract

The maximal ADM mass for (mini-)boson stars (BSs) -- gravitating solitons of Einstein's gravity minimally coupled to a free, complex, mass $μ$ , Klein-Gordon field -- is $M_{ADM}^{max} \sim M_{P l}^{2} / μ$ . Adding quartic self-interactions to the scalar field theory, described by the Lagrangian $L_{I} = λ ∣Ψ ∣^{4}$ , the maximal ADM mass becomes $M_{ADM}^{max} \sim λ M_{P l}^{3} / μ^{2}$ . Thus, for mini-BSs, astrophysically interesting masses require ultra-light scalar fields, whereas self-interacting BSs can reach such values for bosonic particles with Standard Model range masses. We investigate how these same self-interactions affect Kerr black holes with scalar hair (KBHsSH) [1], which can be regarded as (spinning) BSs in stationary equilibrium with a central horizon. Remarkably, whereas the ADM mass scales in the same way as for BSs, the \textit{horizon mass} $M_{H}$ does not increases with the coupling $λ$ , and, for fixed $μ$ , it is maximized at the "Hod point", corresponding to the extremal Kerr black hole obtained in the vanishing hair limit. This mass is always $M_{H}^{max} \sim M_{Pl}^{2} / μ$ . Thus, introducing these self-interactions, the black hole spacetimes may become considerably "hairier" but the trapped regions cannot become "heavier". We present evidence this observation also holds in a model with $L_{I} = β ∣Ψ ∣^{6} - λ ∣Ψ ∣^{4}$ ; if it extends to \textit{general} scalar field models, KBHsSH with astrophysically interesting horizon masses \textit{require} ultra-light scalar fields. Their existence, therefore, would be a smoking gun for such (beyond the Standard Model) particles.

Kerr black holes with self-interacting scalar hair: hairier but not heavier

Abstract

References in corpus (18)

Cited by in corpus (100)