# No-hair theorems for a static and stationary reflecting star

## TL;DR

This paper extends no-hair theorems to static and stationary reflecting stars, proving the non-existence of scalar, vector, and tensor hairs outside their surfaces, including cases with a positive cosmological constant.

## Contribution

It generalizes the no-hair theorem from black holes to horizonless reflecting stars and includes cases with a positive cosmological constant.

## Key findings

- No massive scalar, vector, or tensor hairs exist outside reflecting stars.
- The theorem applies to both static and stationary configurations.
- Results extend to spacetimes with positive cosmological constant.

## Abstract

We prove the non existence of massive scalar, vector and tensor hairs outside the surface of a static and stationary compact reflecting star. Our result is the extension of the no hair theorem for black holes to horizonless compact configurations with reflecting boundary condition at the surface. We also generalize the proof for spacetimes with a positive cosmological constant.