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

TL;DR

This paper develops a method to accurately compute gravitational wave energy in ghost-free bigravity, addressing ambiguities caused by additional degrees of freedom and enabling future waveform modeling in this theory.

Contribution

It introduces a canonical current formalism to unambiguously calculate gravitational wave energy in bigravity, a significant step for waveform predictions beyond general relativity.

Findings

Canonical current formalism yields unambiguous energy calculations in bigravity.

The method aligns with GR energy calculations, ensuring consistency.

Facilitates future gravitational waveform modeling in bigravity.

Abstract

One of the key ingredients for making binary waveform predictions in a beyond-GR theory of gravity is understanding the energy and angular momentum carried by gravitational waves and any other radiated fields. 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 the new degrees of freedom and length scales which are not present in GR, rendering an Isaacson-style averaging calculation ambiguous. In this article we compute the energy carried by gravitational waves 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), making it a convenient choice for quantifying the energy of gravitational waves in bigravity or any diffeomorphism-invariant theories of gravity. This calculation opens the door for future waveform modeling in bigravity to correctly include backreaction due to emission of gravitational waves.