# Regular scalar field around reflecting stars and black holes, and reflecting star polarization

## TL;DR

This paper investigates the existence and properties of regular scalar fields around reflecting stars and black holes, revealing that reflecting stars can become polarized due to scalar sources, unlike black holes.

## Contribution

It introduces conditions for regular scalar fields around reflecting stars and compares these with black hole cases, highlighting polarization effects.

## Key findings

- Reflecting stars can support regular non-trivial scalar fields.
- Scalar charge is determined for reflecting stars with conformal coupling.
- Reflecting stars become polarized in the presence of scalar sources.

## Abstract

The existence of a regular non-trivial scalar field in the background of an asymptotically flat static reflecting star is discussed. The scalar field is assumed to be conformally coupled to the outside matter. The induced scalar charge is determined and the required conditions to have regular field are obtained. The results are compared with the case of a black hole. Conditions to have regular non-trivial scalar field out of the black hole horizon are investigated. We show that in the presence of a scalar source, in contrast to the black holes, the reflecting star becomes polarized.