Gravitoelectromagnetic Knot Fields

Abstract

We construct a class of knot solutions of the gravitoelectromagnetic (GEM) equations in vacuum in the linearized gravity approximation by analogy with the Rañada–Hopf fields. For these solutions, the dual metric tensors of the bi-metric geometry of the gravitational vacuum with knot perturbations are given and the geodesic equation as a function of two complex parameters of the GEM knots are calculated. Finally, the Landau–Lifshitz pseudo-tensor and a scalar invariant of the GEM knots are computed.

A complementary covariant approach to gravito-electromagnetism

“…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.…”