# Hair-dressing Horndeski: an approach to hairy solutions in cubic Horndeski gravity

## TL;DR

This paper introduces a reverse engineering method in cubic Horndeski gravity to derive models supporting specific solutions, leading to new hairy black hole solutions and analyzing their properties.

## Contribution

It develops a novel approach to find models from desired solutions in cubic Horndeski gravity, including the discovery of a new hairy black hole.

## Key findings

- Derived exact static, spherically symmetric solutions in cubic Horndeski gravity.
- Constructed a new hairy black hole solution and analyzed its properties.
- Discussed the method's limitations and potential extensions.

## Abstract

In obtaining exact solutions in gravitational theories containing arbitrary model functions, such as Horndeski gravity, one usually starts by prescribing the model functions of the theory and then goes on to solving their corresponding field equations. In this paper, we explore the extent to which the reverse procedure can be useful, whereby one starts with desired solutions and then determines the models that support them. Working within the phenomenologically interesting cubic and shift-symmetric sector of Horndeski gravity, we develop a method for obtaining exact static and spherically-symmetric solutions, one of which happens to be a new hairy black hole. We study this black hole and its properties. We also discuss the limitations of the method and its possible extension to other Horndeski sectors.