Trapping and Guiding Bodies by Gravitational Waves Endowed with Angular Momentum

Abstract

Trapping of bodies by waves is extended from electromagnetism to gravity. It is shown that gravitational waves endowed with angular momentum may accumulate near its axis all kinds of cosmic debris. The trapping mechanism in both cases can be traced to the Coriolis force associated with the local rotation of the space metric. The same mechanism causes the Trojan asteroids to librate around the Sun-Jupiter stable Lagrange points L4 and L5. Trapping of bodies in the vicinity of the wave center could also be related to the formation of galactic jets. FIG. 1. Projection of the trajectory on the xy plane for a charged particle trapped by the electromagnetic wave (left) and for a massive particle trapped by the gravitational wave (right). The parameters in the gravitational case were chosen to show the correspondence with the electromagnetic case and not to describe a realistic situation.It has been established in Refs. [1-3] that electromagnetic waves endowed with angular momentum (for example, Bessel beams) can trap charged particles in the vicinity of the beam center. In this Letter we prove that the gravitational waves carrying angular momentum have the same property. In Fig.1 we plotted the projection of the particle orbit onto the plane perpendicular to the beam direction for the electromagnetic and the gravitational case. The close similarity between the two plots is the best proof that in both case we are dealing with very similar phenomena. The mechanism which is responsible for trapping of bodies near the center of the gravitational wave is the same as that encountered in many diverse physical systems: it is the Coriolis force. This force leads to stable orbits of Trojan asteroids [4] and ions in the Paul trap [5], to stable wave packets of electrons in high Rydberg states moving in a circularly polarized electromagnetic wave [6] and electrons in rotating molecules [7].The angular momentum production for compact binaries in the final stages of their merger is huge. In the simplest case of two equal masses m in circular orbits with the radius R, the angular momentum luminosity iswhere R S is the Schwarzschild radius for mass m. For example, for two black holes having 30 solar masses inspiraling at a distance of 10 R S the gravitational radiation carries away every second about six million times the angular momentum of the Earth in its orbital motion. In contrast to the electromagnetic case, the trapping in the gravitational case is universal; it does not depend on the mass of the body. The simplest model of a gravitational wave carrying angular momentum is the Bessel beam. Bessel beams are non-diffractive; they have the same width along the direction of propagation which is usually chosen as the direction of the z axis. The Riemann tensor for Bessel beams in the weak field approximation has been obtained in [9]. Its components can be constructed [10] from the components of the rank-four symmetric spinor φ ABCD :where S AB µν are built from Pauli matrices,{S 23 , S 31 , S 12 } = i{S 01 , S 02 , S 03 }.The sign ...

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