Post-Newtonian Theory and Dimensional Regularization

TL;DR

This paper discusses the application of dimensional regularization in post-Newtonian theory to accurately model gravitational waves from inspiralling compact binaries, resolving previous ambiguities in high-order calculations.

Contribution

It introduces dimensional self-field regularization within general relativity, successfully fixing all ambiguity parameters in 3PN gravitational wave calculations.

Findings

Dimensional regularization resolves ambiguity parameters in 3PN calculations.

High-accuracy templates for gravitational wave detection are improved.

The method enhances the theoretical foundation for gravitational wave modeling.

Abstract

Inspiralling compact binaries are ideally suited for application of a high-order post-Newtonian (PN) gravitational wave generation formalism. To be observed by the LIGO and VIRGO detectors, these very relativistic systems (with orbital velocities of the order of 0.5c in the last rotations) require high-accuracy templates predicted by general relativity theory. Recent calculations of the motion and gravitational radiation of compact binaries at the 3PN approximation using the Hadamard self-field regularization have left undetermined a few dimensionless coefficients called ambiguity parameters. In this article we review the application of dimensional self-field regularization, within Einstein's classical general relativity formulated in D space-time dimensions, which finally succeeded in clearing up the problem, by uniquely fixing the values of all the ambiguity parameters.