hairy black holes, boson stars and non-minimal couplings from Einstein to teleparallel gravity

Alternative theories of gravity including a scalar field have attracted a lot of attention in the past decade. This is especially true for Horndeski gravity; the most general scalar-tensor theory of gravity in 4D, based on the same geometrical framework as GR, including a real scalar field and presenting second order field equations.

The aim of this talk is to present some of the main results obtained during my PhD thesis under the supervision of Yves Brihaye and related to the topic of spherically symmetric compact objects endowed with scalar fields.
First, I will present some results obtained with Yves in the context of Horndeski gravity. More precisely, I will comment on solutions obtained numerically in a subsector of Horndeski gravity where a scalar field is non-minimally coupled to the Gauss-Bonnet invariant. In particular, I will try to emphasise how the hairy black hole solutions obtained in this context generalised results already known in the literature.
Second, I will introduce recent results of my research in the context of teleparallel theories of gravity. I will start by a short synopsis of the main features of teleparallel theories of gravity compared to metric based theories (especially GR). I will then discuss recent results regarding hairy black holes for some teleparallel theories of gravity endowed with a non-minimally coupled real scalar field.

If time permits, I will comment on how one could possibly extend results obtained for metric based scalar-tensor theories of gravity using the framework of teleparallel gravity.