Stationary bound-state scalar configurations supported by rapidly-spinning exotic compact objects

Some quantum-gravity theories suggest that the absorbing horizon of a classical black hole should be replaced by a reflective surface which is located a microscopic distance above the would-be classical horizon. Instead of an absorbing black hole, the resulting horizonless spacetime describes a reflective exotic compact object. Motivated by this intriguing prediction, in the present paper we explore the physical properties of exotic compact objects which are linearly coupled to stationary bound-state massive scalar field configurations. In particular, solving the Klein-Gordon wave equation for a stationary scalar field of proper mass μ and spheroidal harmonic indices (l,m) in the background of a rapidly-rotating exotic compact object of mass M and angular momentum J=Ma, we derive a compact analytical formula for the discrete radii {rc(μ,l,m,M,a;n)} of the exotic compact objects which can support the stationary bound-state massive scalar field configurations. We confirm our analytical results by direct numerical computations.