Balance laws as test of gravitational waveforms

Gravitational waveforms play a crucial role in comparing observed signals with theoretical predictions. However, obtaining accurate analytical waveforms directly from general relativity (GR) remains challenging. Existing methods involve a complex blend of post-Newtonian theory, effective-one-body formalism, numerical relativity and interpolation, introducing systematic errors. As gravitational wave astronomy advances with new detectors, these errors gain significance, particularly when testing GR in the nonlinear regime. A recent development proposes a novel approach to address this issue. By deriving precise constraints-or balance laws-directly from full nonlinear GR, this method offers a means to evaluate waveform quality, detect template weaknesses and ensure internal consistency. Before delving into the intricacies of balance laws in full nonlinear GR, we illustrate the concept using a detailed mechanical analogy. We will examine a dissipative mechanical system as an example, demonstrating how mechanical balance laws can gauge the accuracy of approximate solutions in capturing the complete physical scenario. While mechanical balance laws are straightforward, deriving balance laws in electromagnetism and GR demands a rigorous foundation rooted in mathematically precise concepts of radiation. Following the analogy with electromagnetism, we derive balance laws in GR. As a proof of concept, we employ an analytical approximate waveform model, showcasing how these balance laws serve as a litmus test for the model's validity. This article is part of the theme issue 'The particle-gravity frontier'.