Magnetic effects in general relativity: Quadrupoles, shear, and memory

Abstract

Gravitational effect of "magnetic type" -- those having a curl-like character over large spheres -- are investigated, for isolated systems. The Bondi-Sachs-Newman-Penrose formalism clarifies a number of points, especially related to radiation memory. It is shown that the "memory tensor" is equivalent to the change in Bondi shear, from before to after the emission of radiation. This means that if magnetic radiation memory is present, at least one of the intervals bracketing the radiation must have non-zero magnetic shear but vanishing radiation. Such intervals, called here CPMS regimes, are shown to be necessarily non-stationary, however, raising a variety of technical and interpretative issues. In linearized general relativity, the gravitational fields due to point magnetic quadrupoles with arbitrary time-dependence are computed, and some of their physics studied. In the far zone, there is a red-shift effect which could be searched for astrophysically: light coming from behind a source generating magnetic shear would be red-shifted by an amount varying with the angle around the source of shear, and in the far-field limit this red-shift goes inversely with the impact parameter. Induction-zone effects are also considered. An induction-zone memory effect should exist which could possibly be within the reach of laboratory experiments, but no good candidates for astrophysically detectable effects are found. Also a quadrupole will induce test particles to move in such a fashion as to create an opposing quadrupole, an effect reminiscent of Lenz's law.