A Novel Covariant Approach to Gravito-Electromagnetism

Abstract

This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. 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.

A complementary covariant approach to gravito-electromagnetism

“…Equations ( 7) are identical to that proposed in Ref. [2], while (8) has a single difference, a flipped sign on of the second term. The ultimate proposal of the present article is to determine the differences concerning this single difference.…”

“…In this article, we propose an exercise concerning a recently published gravitation theory that modifies GR within the gravito-electromagnetic precision order [2]. In summary, we will analyze an alternative to this previously proposed modified theory in order to exhaust the possible alterations that are coherent to the original idea.…”

“…Independently of this feature, the conceptual idea of GEM evidences the parallel between electromagnetism and gravitation, and various ideas to implement the gravito-electromagnetic approximation have been elaborated, and a list of references of them can be found in Refs. [2,[9][10][11]. In Ref.…”

“…In Ref. [2], the gravitational field g g g was decomposed as a sum of two auxiliary fields, the gravito-electric field g g g E and the gravito-magnetic field g g g B , where…”

“…Additionally, we will confirm that the gravitational field given by ( 7) has a physical content comparable to that achieved after the truncation of Eintein's field equations. We remember that truncation of Einstein's equations generates the Newtonian theory at its first approximation, while higher order terms produce (2)(3)(4), and this prevision of GR will be recovered from Eq. ( 7) using a covariant scheme.…”