Renormalisation Group approach to General Relativity
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. After demonstrating that our equation correctly reproduces the Post-Minkowskian expansion, we show how it easily recovers the 1PN two-body action, bypassing the need for complex three-graviton vertex calculations. This establishes the exact RG as a powerful new tool for tackling strong-field dynamics in gravity.
Cite
@article{arxiv.2510.27676,
title = {Renormalisation Group approach to General Relativity},
author = {F. Gutiérrez and K. Falls and A. Codello},
journal= {arXiv preprint arXiv:2510.27676},
year = {2026}
}