# Linearization of Moffat's Symmetric Complex Metric Gravity

## TL;DR

This paper explores the linearized equations of a complex symmetric extension of general relativity, revealing a complex gravitomagnetism and discussing gravitational waves within this theoretical framework.

## Contribution

It derives the linearized field equations of Moffat's symmetric complex metric gravity using two approaches and discusses their implications for gravitomagnetism and gravitational waves.

## Key findings

- Linearized equations lead to a complex form of gravitomagnetism.
- Derived gravitational wave equations from the symmetric complex metric theory.
- Discussed open problems in the context of complex gravity theories.

## Abstract

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.