Gravitational Wave Memory Beyond General Relativity

Gravitational wave memory is a non-oscillatory correction to the gravitational wave strain predicted by general relativity, which has yet to be detected. Within general relativity, its dominant component, known as the null memory, can be understood as arising from the back-reaction of the energy carried by gravitational waves, and therefore it corresponds to a direct manifestation of the non-linearity of the theory. In this paper, we investigate the null memory prediction in a broad class of modified gravity theories, with the aim of exploring potential lessons to be learned from future measurements of the memory effect. Based on Isaacson's approach to the leading-order field equations, we in particular compute the null memory for the most general scalar-vector-tensor theory with second order equations of motion and vanishing field-potentials. We find that the functional form of the null memory is only modified through the potential presence of additional radiative null energy sources in the theory. We subsequently generalize this result by proving a theorem that states that the simple structure of the tensor null memory equation remains unaltered in any metric theory whose massless gravitational fields satisfy decoupled wave equations to first order in perturbation theory, which encompasses a large class of viable extensions to general relativity.