# Compact binary coalescences: Constraints on waveforms

## TL;DR

This paper introduces a new method based on general relativity constraints to evaluate and improve the accuracy of gravitational waveforms for compact binary coalescences, crucial for future detector sensitivity.

## Contribution

It proposes using GR constraints as a novel tool to assess and cross-check waveform accuracy beyond current numerical relativity comparisons.

## Key findings

- GR constraints impose infinite conditions on waveforms
- Provides a new external validation method for waveforms
- Helps identify systematic errors in simulations

## Abstract

Gravitational waveforms for compact binary coalescences (CBCs) have been invaluable for detections by the LIGO-Virgo collaboration. They are obtained by a combination of semi-analytical models and numerical simulations. So far systematic errors arising from these procedures appear to be less than statistical ones. However, the significantly enhanced sensitivity of the new detectors that will become operational in the near future will require waveforms to be much more accurate. This task would be facilitated if one has a variety of cross-checks to \emph{evaluate} accuracy, particularly in the regions of parameter space where numerical simulations are sparse. Currently errors are estimated by comparing the candidate waveforms with the numerical relativity (NR) ones, which are taken to be exact. The goal of this paper is to propose a qualitatively different tool. We show that full non-linear general relativity (GR) imposes an infinite number of sharp constraints on the CBC waveforms. These can provide clear-cut measures to evaluate the accuracy of candidate waveforms against exact GR, help find systematic errors, and also provide external checks on NR simulations themselves.