Variational Closure of Finite Einstein-Standard-Model Actions
Abstract
We establish conditions under which a finite gravity-matter system with Lorentzian geometry, Standard-Model field content, and a common variational principle has the classical Einstein-Standard-Model equations as its continuum limit. We formulate a minimal finite gravity-matter interface and prove a subsequential variational closure theorem: compactness, first-variation consistency, and physically scaled stationarity imply the coupled Einstein-Yang-Mills-Higgs-Dirac-Yukawa equations in distributions. On a regular branch, Sobolev estimates yield the required bosonic compactness, while Lorentzian symmetric-hyperbolic stability gives strong spinor H1 compactness. For an explicit finite common action, we further obtain quantitative convergence of the reconstructed fields, curvature, and complete Standard-Model stress. When strong bosonic compactness fails, Yang-Mills and Higgs oscillation or concentration survive in the limit as explicit stress defects. Renewal Geometry provides one finite realization of the interface, while the continuum closure arguments depend only on the stated structural and analytic hypotheses.
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BibTeX
@misc{pelissier2026variational,
title = {{Variational Closure of Finite Einstein-Standard-Model Actions}},
author = {Aurelien Pelissier},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05755431v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Variational Closure of Finite Einstein-Standard-Model Actions
AU - Aurelien Pelissier
PY - 2026
DA - 2026/09/19
PB - HAL
UR - https://hal.science/hal-05755431v1
AB - We establish conditions under which a finite gravity-matter system with Lorentzian geometry, Standard-Model field content, and a common variational principle has the classical Einstein-Standard-Model equations as its continuum limit. We formulate a minimal finite gravity-matter interface and prove a subsequential variational closure theorem: compactness, first-variation consistency, and physically scaled stationarity imply the coupled Einstein-Yang-Mills-Higgs-Dirac-Yukawa equations in distributions. On a regular branch, Sobolev estimates yield the required bosonic compactness, while Lorentzian symmetric-hyperbolic stability gives strong spinor H1 compactness. For an explicit finite common action, we further obtain quantitative convergence of the reconstructed fields, curvature, and complete Standard-Model stress. When strong bosonic compactness fails, Yang-Mills and Higgs oscillation or concentration survive in the limit as explicit stress defects. Renewal Geometry provides one finite realization of the interface, while the continuum closure arguments depend only on the stated structural and analytic hypotheses.
ER -