# No hair theorem for massless scalar fields outside asymptotically flat horizonless reflecting compact stars

## TL;DR

This paper provides a rigorous proof that massless scalar fields cannot exist outside certain horizonless, reflecting compact stars, extending the no hair theorem to these objects.

## Contribution

It offers the first rigorous mathematical proof that massless scalar fields cannot be supported outside asymptotically flat, horizonless reflecting compact stars.

## Key findings

- Massless scalar fields cannot exist outside these stars.
- The no hair theorem applies to massless scalar fields in this context.
- Supports the uniqueness of such compact star solutions.

## Abstract

In a recent paper, Hod started a study on no scalar hair theorem for asymptotically flat spherically symmetric neutral horizonless reflecting compact stars. In fact, Hod's approach only rules out massive scalar fields. In the present paper, for massless scalar fields outside neutral horizonless reflecting compact stars, we provide a rigorous mathematical proof on no hair theorem. We show that asymptotically flat spherically symmetric neutral horizonless reflecting compact stars cannot support exterior massless scalar field hairs.