  We construct asymptotically AdS black hole solutions, with a self-interacting
bulk scalar field, in the context of 5D general relativity. As the observable
universe is characterized by spatial flatness, we focus to solutions where the
horizon of the black hole, and subsequently all 3D hypersurfaces for fixed
radial coordinate,have zero spatial curvature. We examine two cases for the
black hole scalar hair: a) an exponential decaying scalar field profile and b)
an inverse power scalar field profile. The scalar black hole solutions we
present in this paper, are characterized by four functions f(r), a(r), phi(r)
and V(phi(r)). Only the functions phi(r) and a(r) are determined analytically,
while the functions f(r) and V(phi(r)) are expressed semi-analytically, by
integral formulas in terms of a(r). We present our numerical results in figures
and we study in detail the characteristic properties of our solutions. We also
note that the potential we obtain has a non-convex form in agreement with the
corresponding "no hair theorem" for AdS space-times.

High Energy Physics - Theory