Spontaneous Scalarization of Black Holes in Gauss-Bonnet Teleparallel Gravity

TL;DR

This paper introduces new scalarized black hole solutions within a Teleparallel gravity framework by coupling a scalar field to the Gauss-Bonnet invariant, revealing novel phenomenology distinct from traditional Einstein-Gauss-Bonnet theories.

Contribution

It develops a Teleparallel extension of Gauss-Bonnet gravity, demonstrating scalarized black holes with unique features like non-monotonic metric functions and scalar fields.

Findings

Existence of asymptotically flat scalarized black holes.

Distinct behaviors compared to Einstein-Gauss-Bonnet solutions.

Non-monotonic metric and scalar field profiles.

Abstract

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