Spontaneous scalarization of black holes in Gauss-Bonnet teleparallel gravity

In this paper, we find new scalarized black holes by coupling a scalar field with the Gauss-Bonnet invariant in teleparallel gravity. The formulation of theory uses torsion instead curvature to describe gravitational interaction, and it turns out that, language, usual term four dimensions decays two distinct boundary terms, invariants. Both can be coupled individually or any combination field, obtain extension equivalent general relativity. study contains familiar Riemannian Einstein-Gauss-Bonnet gravity as particular limit offers natural extension, which scalarization is triggered interesting phenomenology. We demonstrate numerically existence asymptotically flat hole solutions show depending on choice they have behavior compared ones known from case. More specifically, nonmonotonicity metric functions present, feature that was not observed until now for static solutions.