# Tests of general relativity at the fourth post-Newtonian order

**Authors:** Poulami Dutta Roy, Sayantani Datta, K. G. Arun  
**arXiv:** [2406.07691](https://arxiv.org/abs/2406.07691)  
**Date:** 2024-06-11  
**Summary page:** https://www.summarizepaper.com/en/paper/2406.07691v1/

## Key points

- The paper focuses on tests of General Relativity at the fourth Post-Newtonian (PN) order in compact binary dynamics.
- It discusses gravitational-wave phasing up to 4.5PN order, including novel physical effects like the tail of the memory and various higher-order moments.
- The study evaluates the testing capabilities of current-generation (2G) detectors like LIGO/Virgo, next-generation (XG) ground-based detectors such as Cosmic Explorer/Einstein Telescope, and space-based detectors like LISA at these PN orders.
- Using the Fisher information matrix, the paper projects bounds on deviations from logarithmic PN phasing coefficients at 4PN for XG and 2G detectors.
- Projected bounds are also provided for three other PN coefficients appearing at 4PN and 4.5PN for XG and 2G detectors, with potential constraints from observations of supermassive black holes by LISA.
- The study explores how total mass and mass ratio impact these bounds for binaries in quasi-circular orbits, serving as unique probes of higher-order nonlinear interactions in compact binary dynamics consistent with General Relativity predictions.
- The paper is organized into sections covering waveform models used, deformation coefficients introduced at 4 and 4.5PN, formalism of the Fisher information matrix for computing bounds on deformation coefficients, results on deformation parameter bounds, and a conclusion.
- An assessment in an appendix compares Fisher-based projections to actual errors based on analyzed detected binaries.

## Summary

The paper discusses tests of General Relativity at the fourth Post-Newtonian (PN) order, with a focus on recently computed gravitational-wave phasing up to 4.5PN order in compact binary dynamics. This includes novel physical effects such as the tail of the memory, tails of tails of tails, and tails of mass hexadecupole and current octupole moments. The study aims to assess the ability of current-generation (2G) detectors like LIGO/Virgo, next-generation (XG) ground-based detectors such as Cosmic Explorer/Einstein Telescope, and space-based detectors like LISA to test PN theory predictions at these orders. Using the Fisher information matrix, this paper projects bounds on deviations from logarithmic PN phasing coefficients at 4PN for XG and 2G detectors. It also provides projected bounds on three other PN coefficients appearing at 4PN and 4.5PN for XG and 2G detectors. Additionally, observations from LISA of supermassive black holes could offer tight constraints on these parameters. The study explores how total mass and mass ratio affect these bounds for binaries in quasi-circular orbits. These tests serve as unique probes of higher-order nonlinear interactions in compact binary dynamics and their consistency with General Relativity predictions. The paper is organized into sections discussing the waveform model used, deformation coefficients introduced at 4 and 4.5PN, formalism of the Fisher information matrix for computing bounds on deformation coefficients, results on deformation parameter bounds, and a conclusion. An assessment is provided in an appendix on how Fisher-based projections may compare to actual errors based on detected binaries that have been analyzed.