Lovelock Galileons and black holes

We study a scalar-tensor version of Lovelock theory with a nontrivial higher-order Galileon term involving the coupling of the Lovelock two tensor with derivatives of the scalar Galileon field. For a static and spherically symmetric spacetime, we extend the Boulware-Deser solution to the presence of a Galileon field. The hairy solution has a regular scalar field on the black hole event horizon and presents certain selftuning properties for the bulk cosmological constant and the Gauss-Bonnet coupling. The combined time and radial dependence of the Galileon field permits its horizon regularity. Furthermore in order to investigate the effects of linear time dependence we find spherically symmetric solutions in four and five spacetime dimensions. They are shown to have singular horizons. Afar from the Schwarzschild radius and for weak higher-dimensional couplings the solutions are perturbatively close to GR representing exteriors of GR-like star solutions for scalar tensor theories.