# A no-hair theorem for stars in Horndeski theories

## TL;DR

This paper proves a no-hair theorem for stars in Horndeski theories, showing that regular, static, spherically symmetric stars cannot support scalar hair due to the vanishing of the Noether current.

## Contribution

It establishes a general no-hair theorem for stars in Horndeski and beyond theories, extending previous results to a broad class of scalar-tensor models.

## Key findings

- No scalar hair for static, spherically symmetric stars in these theories
- The Noether current associated with shift-symmetry vanishes in regular spacetimes
- The theorem's validity is carefully detailed

## Abstract

We consider a generic scalar-tensor theory involving a shift-symmetric scalar field and minimally coupled matter fields. We prove that the Noether current associated with shift-symmetry vanishes in regular, spherically symmetric and static spacetimes. We use this fact to prove the absence of scalar hair for spherically symmetric and static stars in Horndeski and beyond theories. We carefully detail the validity of this no-hair theorem.