  In arbitrary dimension D, we consider a self-interacting scalar field
nonminimally coupled with a gravity theory given by a particular Lovelock
action indexed by an integer k. To be more precise, the coefficients appearing
in the Lovelock expansion are fixed by requiring the theory to have a unique
AdS vacuum with a fixed value of the cosmological constant. This yields to
k=1,2,...,[(D-1)/2] inequivalent possible gravity theories; here the case k=1
corresponds to the standard Einstein-Hilbert Lagrangian. For each par (D,k), we
derive two classes of AdS black hole solutions with planar event horizon
topology for particular values of the nonminimal coupling parameter. The first
family of solutions depends on a unique constant and is valid only for k>1. In
fact, its GR counterpart k=1 reduces to the pure AdS metric with a vanishing
scalar field. The second family of solutions involves two independent constants
and corresponds to a stealth black hole configuration; that is a nontrivial
scalar field together with a black hole metric such that both side of the
Einstein equations (gravity and matter parts) vanishes identically. In this
case, the standard GR case k=1 reduces to the Schwarzschild-AdS-Tangherlini
black hole metric with a trivial scalar field. In both cases, the existence of
these solutions is strongly inherent of the presence of the higher order
curvature terms k>1 of the Lovelock gravity. We also establish that these
solutions emerge from a stealth configuration defined on the pure AdS metric
through a Kerr-Schild transformation. Finally, in the last part, we include
multiple exact (D-1)-forms homogenously distributed and coupled to the scalar
field. For a specific coupling, we obtain black hole solutions for arbitrary
value of the nonminimal coupling parameter generalizing those obtained in the
pure scalar field case.
