Searcharxiv⌕ Search

arXiv subjects

F. Gutiérrez

Publications and source records attributed to F. Gutiérrez.

2 recordsLinked to original sources
arXiv2026

Renormalisation Group approach to General Relativity

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.

gr-qc↗
arXiv2026

Classical Renormalization Group Equations for General Relativity

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.

gr-qc↗