Static scalar field condensation in regular asymptotically AdS reflecting star backgrounds

TL;DR

This paper investigates the conditions under which scalar fields condense around regular asymptotically AdS reflecting stars, establishing bounds on star radii and analyzing the effects of parameters on scalar hair formation.

Contribution

It provides analytical bounds for scalar hairy star radii and numerically constructs solutions, highlighting differences from flat reflecting stars and effects of charge and cosmological constant.

Findings

Scalar hair exists only below a certain star radius bound.

The radii of hairy stars are discrete and depend on parameters.

Scalar condensation is suppressed for small star charge or large negative cosmological constant.

Abstract

We study condensation behaviors of static scalar fields in the regular asymptotically AdS reflecting star spacetime. With analytical methods, we provide upper bounds for the radii of the scalar hairy reflecting stars. Above the bound, there is no scalar hair theorem for the star. Below the bound, we numerically obtain charged scalar hairy reflecting star solutions and in particular, the radii of the hairy stars are discrete, which is similar to known results in other reflecting object backgrounds. For every set of parameters, we search for the largest AdS hairy star radius, study effects of parameters on the largest hairy star radius and also find difference between properties in this AdS reflecting star background and those in the flat reflecting star spacetime. Moreover, we show that scalar fields cannot condense around regular AdS reflecting stars when the star charge is small or the cosmological constant is negative enough.