Spin Angular Momentum Imparted by Gravitational Waves

Following the demonstration that gravitational waves impart linear momentum, it is argued that if they are polarized they should impart angular momentum to appropriately placed 'test rods' in their path. A general formula for this angular momentum is obtained and used to provide expressions for the angular momentum imparted by plane and cylindrical gravitational waves. While the plane [1] and cylindrical [2] gravitational wave metrics are exact solutions of Einstein's field equations (and hence have a zero stress-energy tensor) one would expect them to carry energy. To prove that they do so it was shown [2,3,4] that they impart linear momentum to rest particles in their path. By the corresponding argument [5] for the electromagnetic waves, if they are polarized and possess a net spin, they could be expected to impart angular momentum to 'test rods' (the 1-dimensional extension of test particles) in their path. A formula for the linear momentum imparted to test particles in an arbitrary spacetime had been obtained [6] by using the extended pseudo-Newtonian (eψN)-formalism. It was seen that the formula gave the same result as the previous analysis for the plane gravitational wave [3] and an exact expression for he earlier approximate results for cylindrical gravitational waves [2,4]. Here we use the eψN-formalism to obtain a formula for the angular momentum imparted to test rods in arbitrary spacetimes, which is then applied to the plane and cylindrical gravitational wave metrics. The essence of the ψN-formalism [7] was that the tidal acceleration vector for a test rod, represented by the separation vector l µ moving along a world 1