  For various reasons, it seems necessary to include complex saddle points in
the "Euclidean" path integral of General Relativity. But some sort of
restriction on the allowed complex saddle points is needed to avoid various
unphysical examples. In this article, a speculative proposal is made concerning
a possible restriction on the allowed saddle points in the gravitational path
integral. The proposal is motivated by recent work of Kontsevich and Segal on
complex metrics in quantum field theory, and earlier work of Louko and Sorkin
on topology change from a real time point of view.
