# No hair theorem for spherically symmetric regular compact stars with Dirichlet boundary conditions

## TL;DR

This paper proves a no hair theorem for neutral regular compact stars with scalar fields under Dirichlet boundary conditions and explores conditions for scalar hair existence in charged stars, including numerical solutions.

## Contribution

It establishes a no hair theorem for neutral stars and derives an upper bound for scalar hair existence in charged stars, supported by numerical solutions.

## Key findings

- No hair theorem proven for neutral stars.
- An upper bound for charged star radius is derived.
- Numerical solutions found below the upper bound.

## Abstract

We study scalar condensation in the background of asymptotically flat spherically symmetric regular Dirichlet stars. We assume that the scalar field decreases as the star surface is approached. Under these circumstances, we prove a no hair theorem for neutral regular compact stars. We also extend the discussion to charged regular compact stars and find an upper bound for the charged star radius. Above the upper bound, the scalar hair cannot exist. Below the upper bound, we numerically obtain solutions of scalar hairy charged stars.