Hairy Black Holes from Horndeski Theory

We present an exact static black hole solution of Einstein field equations in the framework of Horndeski Theory by imposing spherical symmetry and choosing the coupling constants in the Lagrangian so that the only singularity in the solution is at $r=0$. The analytical extension is built in two particular domains of the parametric space. In the first domain we obtain a solution exhibiting an event horizon analogous to that of the Schwarzschild geometry. For the second domain, we show that the metric displays an exterior event horizon and a Cauchy horizon which encloses a singularity. For both branches we obtain the corresponding Hawking temperature which, when compared to that of the Schwarzschild black hole, acquires a correction proportional to a combination of the coupling constants. Such a correction also modifies the definition of the entropy of the black hole.