# Nutty black holes in galileon scalar-tensor gravity

## TL;DR

This paper explores new black hole solutions with NUT charge in a scalar-tensor gravity model involving a scalar field coupled to the Gauss-Bonnet term, analyzing their properties and effects on geodesics.

## Contribution

It introduces a two-parameter family of nutty-hairy black holes in scalar-tensor gravity with detailed analysis of their structure and geodesic behavior.

## Key findings

- Existence of nutty-hairy black holes in the model.
- Influence of scalar hair and NUT-charge on geodesics.
- Detailed interior and exterior solution patterns.

## Abstract

Einstein gravity supplemented by a scalar field non-minimally coupled to a Gauss-Bonnet term provides an example of model of scalar-tensor gravity where hairy black holes do exist. We consider the classical equations within a metric endowed with a NUT-charge and obtain a two-parameter family of nutty-hairy black holes. The pattern of these solutions in the exterior and the interior of their horizon is studied in some details. The influence of both -- the hairs and the NUT-charge -- on the lightlike and timelike geodesics is emphasized.