Gravitational-wave energy and other fluxes in ghost-free bigravity*

Energy and angular momentum fluxes are key ingredients for making binary waveforms. Identifying the appropriate energy functional is unclear in Hassan-Rosen bigravity, a ghost-free theory with one massive and one massless graviton. The difficulty arises from new degrees of freedom and length scales not present in GR, rendering an Isaacson-style averaging calculation ambiguous. We compute the energy carried by gravitational waves (GWs) in bigravity starting from the action, using the canonical current formalism. The canonical current agrees with other common energy calculations in GR, and is unambiguous (modulo boundary terms). This makes it a good choice for quantifying the GW energy in bigravity or any diff-invariant theory of gravity. Our calculation opens the door for future waveform modeling in bigravity to correctly include backreaction due to emission of gravitational waves.