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 postmerger signal of a binary neutron star merger, or of a core collapse supernova.

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• Gravitational waves