Electromagnetism, as unified by James Clerk Maxwell, brought together electricity and magnetism into a single coherent framework that remains foundational to modern physics. The mathematical structure of Maxwell’s equationshas since inspired attempts to describe gravitational phenomena in analogous terms. Early efforts in gravitomagnetism3, as well as studies of gravitomagnetic effects 4, have revealed deep structural connections between gravitational and electromagnetic forces. In particular, gravitomagnetism describes how moving masses—especially rotatingones—interact with spacetime in a manner that mathematically mirrors how moving electric charges generate magnetic fields. These effects have been confirmed experimentally by Gravity Probe B 2 and by satellite laser-rangingexperiments using LARES and LAGEOS 1.In this preprint, we begin constructing a formulation of gravitational magnetism using vector calculus, providinga more direct and accessible framework compared to existing gravitomagnetic treatments in the literature 3, 4. Wefocus on the first of what will be a set of governing equations, establishing the static gravitational Gauss’s law as thefoundation. Subsequent work will extend this to include time-dependent and rotational effects.
Furkan Nar (Sat,) studied this question.