Boson stars and black holes with (complex and) real scalar hair

TL;DR

This paper explores new solutions involving boson stars and black holes with scalar hair, where scalar fields interact via a Hénon-Heiles potential, revealing conditions for their existence and thermodynamic preferences.

Contribution

It introduces models of boson stars and black holes with scalar hair interacting through a Hénon-Heiles potential, showing new solution branches and thermodynamic properties.

Findings

Black holes and boson stars with only a real scalar field are possible.

Black holes with both real and complex scalar fields branch off at large interactions or horizon radius.

Solutions with both fields can be thermodynamically preferred at high temperatures.

Abstract

We discuss boson stars and black holes with scalar hair in a model where the complex scalar field forming the boson star and the hair on the black hole, respectively, interacts with a real scalar field via a H\'enon-Heiles-type potential. We demonstrate that black holes and boson stars carrying only a real scalar field with cubic self-interaction are possible and that black holes with both real and complex scalar field branch off from these solutions for sufficiently large interaction between the two fields and/or sufficiently large horizon radius $r_h$. The latter possess lower mass for the same choice of coupling constants than the former, however seem to be thermodynamically preferred only for high enough temperature.