Linearization of Moffat’s Symmetric Complex Metric Gravity

In this paper we investigate a complex symmetric generalization of general relativity and in particular we investigate its linearized field equations. We begin by reviewing some basic definitions and structures in Moffat’s symmetric complex metric field theory of gravity. We then move on to derive the linearized retarded complex field equations. In addition to this we also derive a linearization of Moffat’s field equations based on the more rigorous Fermi coordinate approach. In conclusion it is shown that the linearized symmetric complex field equations leads to a complex form of gravitomagnetism. We also briefly review the gravitational wave equation from the source less linearized symmetric complex field equations and discuss some open problems.