Novel Ansatzes and Scalar Quantities in Gravito-Electromagnetism

TL;DR

This paper introduces new metric perturbations in Gravito-Electromagnetism that replicate Maxwell's equations and Lorentz force, and defines scalar invariants analogous to electromagnetism, enhancing the theoretical framework of GEM.

Contribution

It proposes two novel forms of metric perturbations in GEM that accurately reproduce electromagnetic equations and forces, and introduces new scalar invariants in the linearised theory.

Findings

New GEM ansatz reproduces Maxwell's equations for dynamical potentials.

Alternative ansatz yields Lorentz force matching electromagnetism without extra terms.

Defined scalar invariants using novel gravitational tensors similar to electromagnetic invariants.

Abstract

In this work, we focus on the theory of Gravito-Electromagnetism (GEM) -- the theory that describes the dynamics of the gravitational field in terms of quantities met in Electromagnetism -- and we propose two novel forms of metric perturbations. The first one is a generalisation of the traditional GEM ansatz, and succeeds in reproducing the whole set of Maxwell's equations even for a dynamical vector potential A. The second form, the so-called alternative ansatz, goes beyond that leading to an expression for the Lorentz force that matches the one of Electromagnetism and is free of additional terms even for a dynamical scalar potential \Phi. In the context of the linearised theory, we then search for scalar invariant quantities in analogy to Electromagnetism. We define three novel, 3rd-rank gravitational tensors, and demonstrate that the last two can be employed to construct scalar quantities that succeed in giving results very similar to those found in Electromagnetism. Finally, the gauge invariance of the linearised gravitational theory is studied, and shown to lead to the gauge invariance of the GEM fields E and B for a general configuration of the arbitrary vector involved in the coordinate transformations.