Classical Renormalization Group Equations for General Relativity
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917519173877760 |
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| author | Gutiérrez, F. Falls, K. Codello, A. |
| author_facet | Gutiérrez, F. Falls, K. Codello, A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22037 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classical Renormalization Group Equations for General Relativity Gutiérrez, F. Falls, K. Codello, A. General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 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. |
| title | Classical Renormalization Group Equations for General Relativity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2605.22037 |