Ultra-spinning exotic compact objects supporting static massless scalar field configurations

TL;DR

This paper analytically investigates ultra-spinning horizonless exotic compact objects with super-critical angular momentum, revealing a finite set of supporting radii for static massless scalar fields and identifying the onset of superradiant instabilities.

Contribution

It extends previous work on sub-critical spinning objects by analyzing the properties and scalar field support of super-critical ultra-spinning exotic compact objects.

Findings

Ultra-spinning objects support a finite discrete set of scalar field configurations.

The largest supporting radius indicates the onset of superradiant instability.

Supported scalar field modes are characterized by harmonic indices l and m.

Abstract

Horizonless spacetimes describing highly compact exotic objects with reflecting (instead of absorbing) surfaces have recently attracted much attention from physicists and mathematicians as possible quantum-gravity alternatives to canonical classical black-hole spacetimes. Interestingly, it has recently been proved that spinning compact objects with angular momenta in the sub-critical regime ${\bar a}\equiv J/M^2\leq1$ are characterized by an infinite countable set of surface radii, $\{r_{\text{c}}({\bar a};n)\}^{n=\infty}_{n=1}$, that can support asymptotically flat static configurations made of massless scalar fields. In the present paper we study analytically the physical properties of ultra-spinning exotic compact objects with dimensionless angular momenta in the complementary regime ${\bar a}>1$. It is proved that ultra-spinning reflecting compact objects with dimensionless angular momenta in the super-critical regime $\sqrt{1-[{{m}/{(l+2)}}]^2}\leq|{\bar a}|^{-1}<1$ are characterized by a finite discrete family of surface radii, $\{r_{\text{c}}({\bar a};n)\}^{n=N_{\text{r}}}_{n=1}$, distributed symmetrically around $r=M$, that can support spatially regular static configurations of massless scalar fields (here the integers $\{l,m\}$ are the harmonic indices of the supported static scalar field modes). Interestingly, the largest supporting surface radius $r^{\text{max}}_{\text{c}}({\bar a})\equiv \text{max}_n\{r_{\text{c}}({\bar a};n)\}$ marks the onset of superradiant instabilities in the composed ultra-spinning-exotic-compact-object-massless-scalar-field system.