Anti-de Sitter massless scalar field spacetimes in arbitrary dimensions

Abstract

We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space and the massless scalar field depends only on the radial coordinate. The field equations are decoupled in the general case, and can be solved exactly for the cases when either the cosmological constant vanishes or the base manifold is Ricci flat. We focus on the case of a negative cosmological constant and a Ricci-flat base manifold. 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 nontrivial scalar field. This spacetime is an asymptotically locally anti-de Sitter one when the Ricci-flat base manifold is locally flat. The asymptotic solution for an arbitrary Einstein base manifold is found and the corresponding mass, calculated through the canonical generator of the time-translation invariance, is shown to be finite. The contribution to the mass from the scalar field at infinity is also discussed.

14 pages, 1 figure. Typos corrected

References in corpus (6)

• Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields
• Electrically charged black hole with scalar hair
• Charged C-metric with conformally coupled scalar field
• Thermodynamical properties of hairy black holes in n spacetimes dimensions
• Scalar solitons and the microscopic entropy of hairy black holes in three dimensions
• Static black hole solutions with a self interacting conformally coupled scalar field

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• Exact dynamical AdS black holes and wormholes with a Klein-Gordon field
• Kasner-type singularities and solitons with Lifshitz asymptotics