Answering the parity question for gravitational wave memory

The memory of gravitational waves in asymptotically-flat spacetimes, that are solutions of the Einstein vacuum equations, is of purely electric parity, and no magnetic parity memory can occur. We show this by investigating what happens for various classes of asymptotically-flat Einstein-vacuum spacetimes. This is understood within such spacetimes that have been shown to be stable in the fully nonlinear regime under perturbations away from Minkwoski space. We also lay open the structures at the transition from spacetimes that have a well-defined memory to those for which the memory formula cannot be retrieved due to their specific asymptotic behavior and the divergence of crucial integrals. Moreover, for the Einstein equations coupled to other fields with a common stress-energy, as well as in the cosmological setting, we find that gravitational memory is of electric parity only.