No-scalar-hair theorem for spherically symmetric reflecting stars

TL;DR

This paper proves that spherically symmetric reflecting stars cannot support static scalar field configurations with monotonically increasing potentials, ruling out the existence of scalar hair around such objects.

Contribution

The authors establish a no-scalar-hair theorem for spherically symmetric reflecting stars with monotonically increasing scalar potentials, extending previous no-hair results.

Findings

No static scalar hair exists outside reflecting stars.

Massive scalar fields with increasing potentials cannot be supported.

The theorem applies to a broad class of scalar self-interactions.

Abstract

It is proved that spherically symmetric compact reflecting objects cannot support static bound-state configurations made of scalar fields whose self-interaction potential $V(\psi^2)$ is a monotonically increasing function of its argument. Our theorem rules out, in particular, the existence of massive scalar hair outside the surface of a spherically symmetric compact reflecting star.