Department of Mechanical Systems Engineering, Technical University of Cluj-Napoca, 103–105 Muncii Bld., C.P. 400641 Cluj-Napoca, Romania
Cresus Godinho
Group of Theoretical Physics and Mathematical Physics, Department of Physics, Federal Rural University of Rio de Janeiro, Cx. Postal 23851, BR 465 Km 7, Seropédica 23890-000, Brazil
Ion Vancea
Group of Theoretical Physics and Mathematical Physics, Department of Physics, Federal Rural University of Rio de Janeiro, Cx. Postal 23851, BR 465 Km 7, Seropédica 23890-000, Brazil
We construct a class of knot solutions of the time-dependent 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 time-dependent GEM knots are calculated. By taking stationary potentials, which formally amount to particularizing to time-independent GEM equations, we obtain a set of stationary fields subjected to constraints from the time-dependent GEM knots. Finally, the Landau–Lifshitz pseudo-tensor and a scalar invariant of the static fields are computed.
