Complex electromagnetism and coupled gravitational-electromagnetic waves in the interstellar medium

Gravito-electromagnetism is an approximation of general relativity that has significant analogies to electromagnetism. We show that the remained asymmetry in those two field equations and the equations of motion can be alleviated through appropriate scaling on the complex plane, thereby allowing gravity and electromagnetism to be combined into a single set of equations for analysis. This enables a more concise and intuitive interpretation of mixed-field interactions of the interstellar medium. The interstellar medium, composed of ionized gas, interacts with both gravitational and electromagnetic fields, and within this medium, gravitational and electromagnetic waves exist in a coupled form. We derive the dispersion relation of these coupled waves tied by the interstellar medium and discuss two branches of wave solutions. These two solutions correspond to the well-known pure gravitational and electromagnetic waves in the classical limit. Based on the characteristics of this coupled wave, we discuss the possible generation of gravitational waves in the interstellar medium and the abnormal behaviors in a medium composed of dark matter that may provide a new methodology for dark matter detection.