Title: Exact solutions of Einstein gravity with a negative cosmological constant coupled to a massless scalar field in arbitrary spacetime dimensions
Abstract: Static d-dimensional spacetimes in Einstein gravity with a negative cosmologicalconstant in the presence of a minimally coupled massless scalar field areconsidered. The spacetimes have a (d − 2)-dimensional transverse space-likesection given by an Einstein Ricci-flat space and the massless scalar fielddepends only on the radial coordinate. The field equations are decoupled andsolved exactly. The solution has a curvature singularity located at the origin,where also the scalar field diverges. Since there is no event horizonsurrounding this singularity, the solution describes a naked singularity dressedwith a non-trivial scalar field. This spacetime is an asymptotically locallyanti-de Sitter one when the Ricci-flat 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 scalarfield, and it is shown to be finite. The contribution of the scalar field atinfinity to the mass is also discussed.
Publication Year: 2012
Publication Date: 2012-04-01
Language: en
Type: article
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