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

2015; American Physical Society; Volume: 92; Issue: 8 Linguagem: Inglês

10.1103/physrevd.92.084059

1550-7998

Carlos Herdeiro, Eugen Radu, Helgi Freyr Rúnarsson,

Pulsars and Gravitational Waves Research

The maximal Arnowitt-Deser-Misner (ADM) mass for (mini)boson stars (BSs)---gravitating solitons of Einstein's gravity minimally coupled to a free, complex, mass $\ensuremath{\mu}$, Klein-Gordon field---is ${M}_{\mathrm{ADM}}^{\mathrm{max}}\ensuremath{\sim}{M}_{\text{Pl}}^{2}/\ensuremath{\mu}$. Adding quartic self-interactions to the scalar field theory, described by the Lagrangian ${\mathcal{L}}_{I}=\ensuremath{\lambda}|\mathrm{\ensuremath{\Psi}}{|}^{4}$, the maximal ADM mass becomes ${M}_{\mathrm{ADM}}^{\mathrm{max}}\ensuremath{\sim}\sqrt{\ensuremath{\lambda}}{M}_{\text{Pl}}^{3}/{\ensuremath{\mu}}^{2}$. Thus, for mini-BSs, astrophysically interesting masses require ultralight 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) [C. A. R. Herdeiro and E. Radu, Kerr Black Holes with Scalar Hair, Phys. Rev. Lett. 112, 221101 (2014).], 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 horizon mass ${M}_{H}$ does not increases with the coupling $\ensuremath{\lambda}$, and, for fixed $\ensuremath{\mu}$, it is maximized at the ``Hod point,'' corresponding to the extremal Kerr black hole obtained in the vanishing hair limit. This mass is always ${M}_{\mathrm{H}}^{\mathrm{max}}\ensuremath{\sim}{M}_{\text{Pl}}^{2}/\ensuremath{\mu}$. Thus, introducing these self-interactions, the black hole spacetimes may become considerably ``hairier'' but the trapped regions cannot become ``heavier.'' We present evidence that this observation also holds in a model with ${\mathcal{L}}_{I}=\ensuremath{\beta}|\mathrm{\ensuremath{\Psi}}{|}^{6}\ensuremath{-}\ensuremath{\lambda}|\mathrm{\ensuremath{\Psi}}{|}^{4}$; if it extends to general scalar field models, KBHsSH with astrophysically interesting horizon masses require ultralight scalar fields. Their existence, therefore, would be a smoking gun for such (beyond the Standard Model) particles.