# No scalar hair theorem for neutral Neumann stars: static massive scalar fields nonminimally coupled to gravity

## TL;DR

This paper demonstrates that Neumann boundary condition compact stars cannot support static massive scalar fields with nonminimal coupling, extending no hair theorems beyond Dirichlet conditions.

## Contribution

It proves the nonexistence of scalar hair for Neumann boundary condition compact stars with nonminimal coupling, generalizing previous no hair theorems.

## Key findings

- Neumann stars cannot support static massive scalar fields.
- Scalar hair is excluded for nonminimal coupling under Neumann conditions.
- Results extend no hair theorems to new boundary conditions.

## Abstract

In a recent paper, Hod proved that spherically symmetric Dirichlet reflecting compact stars cannot support static nonminimally coupled scalar fields. In the present paper, we study the validity of no hair theorems for compact stars with Neumann surface boundary conditions. We find that Neumann compact stars cannot support static massive scalar field hairs with a generic dimensionless nonminimal coupling parameter.