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Non-trivial, static, geodesically complete space-times with a negative cosmological constant II. $n\ge 5$
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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.
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Static vacuum metrics in (4 + 1) dimensions with {\Lambda} < 0 and squashed conformal infinity
Numerical evidence that every squashed three-sphere conformal infinity admits a unique horizonless static vacuum fill-in and a one-parameter family of black-hole fill-ins in 5D AdS.
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