Non-trivial, static, geodesically complete space-times with a negative cosmological constant II. $n\ge 5$

Abstract

We show that the recent work of Lee [23] implies existence of a large class of new singularity-free strictly static Lorentzian vacuum solutions of the Einstein equations with a negative cosmological constant. This holds in all space-time dimensions greater than or equal to four, and leads both to strictly static solutions and to black hole solutions. The construction allows in principle for metrics (whether black hole or not) with Yang-Mills-dilaton fields interacting with gravity through a Kaluza-Klein coupling.

Proceedings of the Strasbourg Meeting on AdS-CFT correspondence, O.Biquard, V.Turaev, Eds., IRMA Lectures in Mathematics and Theoretical Physics, de Gruyter, Berlin, New York, in press; latex2e, 39 pages in A4; minor corrections

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• Domain Structure of Black Hole Space-Times with a Cosmological Constant
• On non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics
• On periodic solutions of nonlinear wave equations, including Einstein equations with a negative cosmological constant