Gravitational wave interactions with matter: beyond quadrupolar perturbations

Previous work has developed the theory of linearized gravitational wave (GW) interactions with matter using the Bondi-Sachs formalism, but with the perturbations restricted to be quadrupolar, i.e., the angular dependence is spherical harmonic with $\ell=2$. Here, the theory is extended to the case of GWs on a Minkowski background with general $\ell$. Formulas for the GW damping and heating effects are obtained for arbitrary $\ell\ge 2$. It is found that the effects are, generally, enhanced, and this suggests that it is unlikely that higher $\ell$-modes will be seen in GW observations of the post-merger signal of a binary neutron star merger, or of a core collapse supernova.