No-short scalar hair theorem for spinning acoustic black holes in a photon-fluid model

Abstract

It has recently been revealed that spinning black holes of the photon-fluid model can support acoustic 'clouds', stationary density fluctuations whose spatially regular radial eigenfunctions are determined by the (2 + 1)-dimensional Klein-Gordon equation of an effective massive scalar field. Motivated by this intriguing observation, we use analytical techniques in order to prove a no-short hair theorem for the composed acoustic-black-hole-scalar-clouds configurations. In particular, it is proved that the effective lengths of the stationary bound-state co-rotating acoustic scalar clouds are bounded from below by the series of inequalities r hair > 1+ √ 5 2