Nonlinear gravito-electromagnetism

Abstract

There is a non-linear and covariant electromagnetic analogy for gravity, in which the full Bianchi identities are Maxwell-type equations for the free gravitational field, encoded in the Weyl tensor. This tensor gravito-electromagnetism is based on a covariant generalization of spatial vector algebra and calculus to spatial tensor fields, and includes all non-linear effects from the gravitational field and matter sources. The non-linear vacuum Bianchi equations are invariant under spatial duality rotation of the gravito-electric and gravito-magnetic tensor fields. The super-energy density and super-Poynting vector of the gravitational field are natural duality invariants, and satisfy a super-energy conservation equation.

Weak gravitational field in Finsler–Randers space and Raychaudhuri equation

“…. Considering in (19) the case where v s = (1, 0, 0, 0) we get the Finslerian potential g 00 of the Randers space for a test material point in the static case…”

“…FR space can play a significant role in the theory of weak field and gravitational waves since "a gravito -electromagnetic field" is intrinsically included in its metric. Einstein's General Relativity shows indeed that gravito -magnetic field may be associated with mass currents [18], [19]. As well a gravito -magnetic force was postulated as an explanation for the anomalous precession of Mercury's perihelion [20].…”

Gravitomagnetism in Teleparallel Gravity

“…26 Finally, we can mention other formulations of GR known as quasiMaxwellian, that is based on a dynamics of the Weyl tensor. [27][28][29] Despite being a fully covariant formalism, it corresponds to a purely formal analogy that associates objects without physical correspondence. 30,31 In the present work, a different approach will be adopted to reexamine gravitomagnetism.…”

On a Lagrangian formulation of gravitoelectromagnetism

“…The symbol · · · denotes the symmetrization of the first and last indices i.e. i and j, in the equations above, and the traceless part of the tensor [34,35]. Henceforth, we work with Gaussian units, c is the speed of light in vacuum, and the metric of flat Minkowski space is given by η μν , is (−1, +1, +1, +1).…”

“…An interesting series of experiments in order to detect gravito-magnetic fields were proposed by Forward [31]. Modern approaches to this analogy and some applications are described in [32][33][34][35][36][37][38]. This description of gravity in analogy with electromagnetism has also been studied with group theoretical methods [39,40].…”