Complex (not because its difficult !), but because certain elements of classical, real GR are allowed to assume complex (real + imag parts) values, such as the metric or connexion. I am wondering if anyone is aware of any legitimate work going on in this area ?? I have already been shanghied by a crackpot's book (blaha's) only to find out that he has never published on this subject either on arxiv or ref.'d journals. The subject is fascinating simply because black hole event horizons become complexified if they exceed `extreme' classification, and go over into naked singularities (NS). Since GR is limited to a real manifold, the problem of NS might become tractable in a complex version of GR... Any thoughts, references ?