  We construct a class of knot solutions of the gravitoelectromagnetic (GEM)
equations in vacuum in the linearized gravity approximation by analogy with the
Ra\~{n}ada-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.
