# On instabilities of stationary scalar field configurations supported by reflecting compact stars

## TL;DR

This paper investigates the stability of scalar fields around horizonless reflecting stars, showing that stationary scalar hairy stars are unstable for low-frequency massless scalar fields, highlighting potential nonlinear instabilities.

## Contribution

It provides theoretical bounds on scalar field frequencies and demonstrates the instability of stationary scalar hairy stars under certain conditions.

## Key findings

- Stationary scalar hairy stars are unstable for low-frequency massless scalar fields.
- Bounds on scalar field frequencies are derived in the probe limit.
- Nonlinear instabilities are expected below certain frequency thresholds.

## Abstract

We study instabilities of the system composed of stationary scalar fields and asymptotically flat horizonless reflecting compact stars. In the probe limit, we obtain bounds on the scalar field frequency. Below this bound, stationary hairy stars are expected to suffer from nonlinear instabilities under massless field perturbations. In other words, we prove that stationary scalar hairy stars are unstable for scalar fields with small frequency.