Gravitoelectromagnetism in teleparallel equivalent of general relativity: A new alternative

Abstract

Spaniol and Andrade introduced grvitoelectromagnetism in TEGR by considering superpotentials, times the determinant of tetrads, as the gravitoelectromagnetic fields. However, since this defined gravitoelectromagnetic field strength does not give rise to a complete set of Maxwell-like equations, we propose an alternative definition of the gravitoelectromagnetic field strength: instead of superpotentials, torsions are taken as the gravitoelectromagnetic field strengths. Based on this new proposal we are able to derive a complete set of Maxwell-like equations. We then apply them to obtain explicit expressions of the gravitoelectromagnetic fields both in Schwarzchilds spacetime and for gravitational waves.

Teleparallel theories of gravity as analogue of nonlinear electrodynamics

“…Here we present the details of the derivation of the teleparallel field equations (32), (37) and (38) in differential form language. We assume that the gravitational action is of the form (31) and hence its variation is given by…”

“…The whole construction can be seen as the gravitational analogue of the so-called premetric generalization of Maxwell electrodynamics [25][26][27][28][29][30], which is part of the framework of premetric electrodynamics. Note that another approach to understand teleparallel gravity in the line of gravitoelectromagnetism can be found in the literature [31,32], while a constitutive relation motivated by continuum mechanics is explored in [33].In this paper we extend the analogy between general theories of electrodynamics and teleparallel gravity, formulated covariantly in terms of constitutive relations, in two directions:…”

Gravitoelectromagnetic Knot Fields

“…Another important property of the GEM knot fields discussed here is the existence of the constraints that must be imposed on the scalar maps due to the gravitational nature of the GEM fields, i.e., Equations (12) above. While the Lorentz gauge is a natural relation among the potential vector components in electromagnetism and, therefore, leads to known properties of the knot fields, the pure GEM constraint is new and emerges in several places in GEM literature.…”

“…These equations establish conditions that the knot maps must satisfy, which are new in the knot fields study. To exemplify, let us consider the second equation from (12) with the second equation for the ansatz (11) in the polar representation. It is easy to see that the following set of equations should be satisfied…”

“…A very large range of fundamental problems have been addressed in the GEM framework. The generalization of the GEM concepts to the non-linear electromagnetism was studied in [8], to the non-commutative geometry in [9], to higher dimensions in [10], to the teleparallel gravity in [11,12] and to the non-local gravity in [13]. By analogy with the quantization of the electromagnetic systems, several quantum aspects of the GEM were investigated in [14][15][16][17].…”