Abstract
Studying a certain sub class of higher order Horndeski (scalar-tensor) theories we discuss a method discovered recently permitting analytic black hole solutions with a non trivial and regular scalar field. One of the solutions found has de Sitter asymptotics and self tunes the bulk cosmological constant. Using the aforementioned method we find and analyse new black hole solutions which can also have de Sitter asymptotics. By looking at small deviations of the integration constant responsible for self tuning we discuss the robustness of the self tuning mechanism. We find that neighboring solutions to the one previously found present also self tuning properties with unaltered effective cosmological constant.
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