A Note On Complex Spacetime Metrics

Understand

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.