Exact solutions of einstein gravity with a negative cosmological constant coupled to a massless scalar -eld in arbitrary spacetime dimensions

Static d-dimensional spacetimes in Einstein gravity with a negative cosmological con- stant in the presence of a minimally coupled massless scalar field are considered. The spacetimes have a (d - 2)-dimensional transverse space-like section given by an Einstein Ricci-At space and the massless scalar field depends only on the radial co- ordinate. The field equations are decoupled and solved exactly. The solution has a curvature singularity located at the origin, where also the scalar field diverges. Since there is no event horizon surrounding this singularity, the solution describes a naked singularity dressed with a non-trivial scalar field. This spacetime is an asymptotically locally anti-de Sitter one when the Ricci-At transverse space has constant curvature. The mass of the solutions is computed using the canonical generator of the time- Translation invariance, as well as the asymptotic form of the metric and scalar field, and it is shown to be nite. The contribution of the scalar field at infinity to the mass is also discussed.