 
Summary: Nontrivial, static, geodesically complete spacetimes
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 singularityfree strictly static Lorentzian vacuum solutions of
the Einstein equations with a negative cosmological constant. This holds
in all spacetime 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 YangMills
dilaton elds interacting with gravity through a KaluzaKlein coupling.
1 Introduction
In recent work [3] we have constructed a large class of nontrivial static, geodesi
cally complete, fourdimensional vacuum spacetimes 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
