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Summary: Non-trivial, static, geodesically complete space-times
with a negative cosmological constant II. n 5
Michael T. Anderson
Piotr T. Chrusciel y
Erwann Delay z
Abstract
We show that the recent work of Lee [24] 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 elds interacting with gravity through a Kaluza-Klein coupling.
1 Introduction
In recent work [3] we have constructed a large class of non-trivial static, geodesi-
cally complete, four-dimensional vacuum space-times with a negative cosmo-
logical constant. The object of this paper is to establish existence of higher
dimensional analogues of the above.
More precisely, we wish to show that for < 0 and n 4 there exist n{
dimensional strictly static 1 solutions (M ; g) of the vacuum Einstein equations
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