AbstractThe duality-symmetric, Maxwell-like, formulation of linearized gravity introduced by Barnett (New J Phys 16, 2014) is used to generalize the conservation laws for helicity, the spin part of angular momentum, and spin-flux, to the case of linearized gravity. These conservation laws have been shown to follow from the conservation property of the helicity array, an analog of Lipkin’s zilch tensor. The analog of the helicity array for linearized gravity is constructed and is shown to be conserved.
AbstractThe set of local gauge invariant quantities for linearized gravity on the Kerr spacetime presented by two of the authors (Aksteiner and Bäckdahl in Phys Rev Lett 121:051104, 2018) is shown to be complete. In particular, any gauge invariant quantity for linearized gravity on Kerr that is local and of finite order in derivatives can be expressed in terms of these gauge invariants and derivatives thereof. The proof is carried out by constructing a complete compatibility complex for the Killing operator, and demonstrating the equivalence of the gauge invariants from Aksteiner and Bäckdahl (Phys Rev Lett 121:051104, 2018) with the first compatibility operator from that complex.
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.
AbstractIt is proved that accelerating nondiffracting gravitational Airy wave-packets are solutions of linearized gravity. It is also showed that Airy functions are exact solutions to Einstein equations for non-accelerating nondiffracting gravitational wave-packets.
Helicity and spin conservation in linearized gravity
