Static Spherically Symmetric solutions in a subclass of Horndeski theories of gravity

TL;DR

This paper explores static spherically symmetric solutions within a specific subclass of Horndeski gravity, identifying black hole solutions and analyzing their thermodynamics, with implications for galaxy rotation curves.

Contribution

It introduces exact black hole solutions in a subclass of Horndeski theories and examines their thermodynamics and potential to explain galaxy rotation curves.

Findings

Found an exact black hole solution with thermodynamic properties similar to General Relativity.

Demonstrated the possibility of reproducing galaxy rotation curves within the model.

Analyzed the thermodynamics using Euclidean Action methodology.

Abstract

In this paper, we will consider a subclass of models of Horndeski theories of gravity and we will check for several Static Spherically Symmetric solutions. We will find a model which admits an exact black hole solution and we will study its thermodynamics by using the Euclidean Action. We will see that, in analogy with the case of General Relativity, the integration constant of the solution can be identified with the mass of the black hole itself. Other solutions will be discussed, by posing a special attention on the possibility of reproducing the observed profiles of the rotation curves of galaxies.