Renormalisation Group approach to General Relativity

TL;DR

This paper introduces an exact renormalization group equation for classical gravitational systems, offering a non-perturbative framework that reproduces known expansions and simplifies calculations in strong-field gravity.

Contribution

It presents the first exact RG approach for classical gravity, capable of reproducing perturbative results and enabling non-perturbative approximations.

Findings

Reproduces first three orders of Post-Minkowskian expansion

Recovers 1PN two-body action efficiently

Provides a new non-perturbative tool for strong-field gravity

Abstract

The detection of gravitational waves has intensified the need for efficient, high-precision modeling of the two-body problem in General Relativity. Current analytical methods, primarily the Post-Minkowskian and Post-Newtonian expansions, are inherently perturbative, while numerical relativity remains computationally expensive. In this Letter, we introduce a middle path: an exact renormalization group (RG) equation for classical gravitational systems. We demonstrate that our equation correctly reproduces the first three orders of the Post-Minkowskian expansion. Crucially, it provides a framework for non-perturbative approximations. As a first application, we show that our method efficiently recovers the 1PN two-body action, bypassing the need for complex three-graviton vertex calculations by leveraging the intrinsic nonlinearity of the RG flow. This establishes the exact RG as a powerful new tool for tackling strong-field dynamics in gravity.