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arXiv · 2605.22037

Classical Renormalization Group Equations for General Relativity

F. Gutiérrez·K. Falls·A. Codello
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Abstract

In a companion paper arXiv:2510.27676, we introduced a non-perturbative classical renormalisation group (RG) flow equation as a novel method for treating strongly interacting problems in general relativity, with a prominent application to the two-body problem. While we demonstrated that it reproduces perturbation theory, via the Post-Minkowskian (PM) expansion, and its computational efficiency in reproducing the 1PN Post-Newtonian action, its derivation was heuristic. In this work, we place this flow equation on a firm formal foundation. In particular, we demonstrate that a Legendre transform maps the classical analogue of the Polchinski equation precisely to our classical RG equation. This establishes a duality between equivalent, exact RG equations for the gravitational effective action. The result, combined with the successful applications in arXiv:2510.27676, solidifies the classical RG framework as a powerful and rigorous new approach to the general relativistic two-body problem and gravitational wave physics.

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BibTeXRIS

F. Gutiérrez, K. Falls, A. Codello. 2026-05-21. Classical Renormalization Group Equations for General Relativity. https://arxiv.org/abs/2605.22037

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