Trapping and Guiding Bodies by Gravitational Waves Endowed with Angular Momentum

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 $L_4$ and $L_5$. Trapping of bodies in the vicinity of the wave center could also be related to the formation of galactic jets.

Figure 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.

Figure 2

The distribution of the $z$ component of angular momentum at 10 wavelengths from the binary system source (solid line) at some given time. Dashed line represents the time averaged distribution. Dotted line represents the Bessel beam $z$-component angular momentum distribution. The horizontal axis is in units of the wavelength.

Figure 3

Reference geodesic (straight line along the $z$ axis) and a nearby geodesic guided by the gravitational wave. The units are not shown in this figure because the size of the curves is arbitrary; it depends solely on the initial conditions. The initial conditions ${\xi }_0={\eta }_R$ and $\gamma =5/36$ are chosen to obtain a strictly periodic motion.