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

TL;DR

This paper derives an analytical formula for the discrete radii of rapidly-spinning exotic compact objects that can support stationary bound-state massive scalar fields, supported by numerical validation.

Contribution

It provides the first explicit analytical expression for the radii of spinning exotic compact objects supporting scalar fields, extending previous numerical studies.

Findings

Derived a compact analytical formula for supporting radii

Confirmed analytical results with numerical computations

Identified conditions for scalar field support on exotic objects

Abstract

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 $\mu$ 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 {\it discrete} radii $\{r_{\text{c}}(\mu,l,m,M,a;n)\}$ 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.