# No hair theorem for bound-state massless static scalar fields outside horizonless Neumann compact stars

## TL;DR

This paper proves that massless static scalar fields cannot form bound states outside horizonless Neumann compact stars, extending previous results for massive fields and contributing to the understanding of no-hair theorems for exotic compact objects.

## Contribution

It establishes a no hair theorem for massless scalar fields outside horizonless Neumann compact stars, filling a gap in the theoretical understanding of scalar field behavior.

## Key findings

- Massless scalar fields cannot form bound states outside these stars.
- The no hair theorem is valid for massless fields, complementing previous results for massive fields.
- The proof applies to asymptotically flat, horizonless, neutral Neumann compact stars.

## Abstract

We study no-hair theorem for horizonless objects, being subject to Neumann boundary conditions. For massive scalar fields, a no hair theorem for Neumann compact stars was proved by us in a previous paper, where the nonzero scalar field mass condition is essential in the proof. In the present work, for massless scalar fields, we prove a no hair theorem, which claims that bound-state massless static scalar fields cannot exist outside asymptotically flat horizonless neutral Neumann compact stars.