Novel ansatzes and scalar quantities in gravito-electromagnetism

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 Φ. 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.

Covariant theory of gravitation in the framework of special relativity

“…and we get the gravitomagnetic homogeneous wave equations. We highlight that (73) shows us clearly that gravitational waves propagate with the speed of the light in vacuum. We remark that this result follows directly from the special theory of relativity and that this result cannot be derived by making a mere analogy between gravitation and electromagnetism, since, in this case, there is no way to guess what should be the gravitational permittivity and permeability of the vacuum.…”

A Novel Covariant Approach to Gravito-Electromagnetism

“…These relationships were observed and reported during the second half of the nineteenth century, and we recommend [1,2] for historical review and references. Various approaches to GEM have recently been proposed, and we quote a non-exhaustive list of papers concerning, by way of example, gravitomagnetic effects [3][4][5][6], the relation of GEM to special relativity [2,7], tidal tensors [8,9], weak-field approximation [10][11][12], the Lorentz violation [13,14], teleparallel gravity [15,16], the Mashhoon-Theiss effect [17], quantum gravity [18,19], gravitational waves [20,21], the relation of GEM to electro-dynamics in curved spacetime [22,23], gravitational field of astrophysical objects [24,25], the Sagnac effect [26,27], torsion gravity [28], the Schrödinger-Newton equation [29], non-commutative geometry [30], spin-gravity coupling [31], gravity and thermodynamics [32], the Casimir effect [33], gauge transformations [34] and, quantum field gravity [35,36]. It is commonly known that GEM is a source of new ideas and a guide for research into new physics.…”

The Mass of the Gravitational Field

“…For more on gravitoelectromagnetism as a limit of general relativity and on the empirical observation of gravitomagnetic effects, see (Forward, [1961]; Braginsky et al, [1977]; Wald, [1984], sec. 4.4a; Harris, [1991]; Damour et al, [1991]; Jantzen et al, [1992]; Ciufolini and Wheeler, [1995]; Maartens and Bassett, [1998]; Mashhoon et al, [1999] Bakopoulos and Kanti, [2017]). In this literature there is wide variation regarding notation and definitions.…”