# A novel covariant approach to gravito-electromagnetism

## TL;DR

This paper introduces a new covariant formulation of gravito-electromagnetism within general relativity, using auxiliary fields and a unified approach to equations of motion and conservation laws.

## Contribution

It presents a novel, unified covariant framework for gravito-electromagnetism involving auxiliary fields and a Lagrangian formulation, advancing theoretical understanding.

## Key findings

- Unified equations of motion and conservation laws
- Introduction of static and moving matter auxiliary fields
- A simple, covariant Lagrangian formulation

## Abstract

This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter field. Equations of motion, continuity equation, energy conservation, field tensor, energy-momentum tensor, constraints and Lagrangian formulation are presented as a simple and unified formulation that can be useful for future research.