A perturbative and gauge invariant treatment of gravitational wave memory

TL;DR

Gravitational wave memory is analyzed within a perturbative, gauge-invariant framework based on the perturbed Weyl tensor. The authors derive memory effects by asymptotically expanding the Weyl tensor near null infinity and integrating the dominant $e_{AB}$ component twice, separating ordinary memory from null memory driven by the energy flux $F$ per solid angle and the change $DeltaP$. They show memory is largely quadrupolar, dominated by the harmonic with ell=2, and that the null memory depends on the angular distribution of radiated energy via $F$. The work is consistent with nonlinear results for electromagnetic and neutrino sources and outlines a path to second-order perturbation theory to capture the gravitational-wave memory beyond first order.

Abstract

We present a perturbative treatment of gravitational wave memory. The coordinate invariance of Einstein's equations leads to a type of gauge invariance in perturbation theory. As with any gauge invariant theory, results are more clear when expressed in terms of manifestly gauge invariant quantities. Therefore we derive all our results from the perturbed Weyl tensor rather than the perturbed metric. We derive gravitational wave memory for the Einstein equations coupled to a general energy-momentum tensor that reaches null infinity.