Balance Laws as Test of Gravitational Waveforms

TL;DR

This paper introduces a new method based on balance laws derived from full non-linear general relativity to evaluate the accuracy and consistency of gravitational waveforms, addressing systematic errors in current models.

Contribution

It develops a novel approach to derive and apply balance laws directly from non-linear GR for testing gravitational waveform quality and internal consistency.

Findings

Balance laws can effectively evaluate waveform accuracy.

The method detects weaknesses in approximate waveform models.

Balance laws serve as a consistency check for gravitational waveforms.

Abstract

Gravitational waveforms play a crucial role in comparing observed signals to theoretical predictions. However, obtaining accurate analytical waveforms directly from general relativity 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 general relativity in the non-linear regime. A recent development proposes a novel approach to address this issue. By deriving precise constraints - or balance laws - directly from full non-linear 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 non-linear general relativity, we illustrate the concept using a detailed mechanical analogy. We'll 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 general relativity demands a rigorous foundation rooted in mathematically precise concepts of radiation. Following the analogy with electromagnetism, we derive balance laws in general relativity. 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.