Boson stars and black holes with complex and real scalar hair

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 rh. 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.