Unification of Gauge Dynamics and Gravitation through Hylodynamics

In this paper, we present a pre-metric continuum framework dubbed "Hylodynamics" in which spacetime metricity, Riemannian curvature, and Yang-Mills gauge dynamics emerge concurrently from the non-linear dynamics of s single master field. The fundamental action is strictly first-order in derivatives, defined over an unmetered four-dimensional manifold $M$ with an indefinite-metric spinor space governed by $\mathfrak{icsl}(2, \mathbb{C}) \subset \mathfrak{su}(2,2)$. Spacetime coordinates possess no prior metric, light cones, or volume measure; soldering along the translation generators pulls back the rigid internal the the Minkowski metric onto the coordinates. Spacetime emerges through this soldering and pull-back. Through the Maurer-Cartan connection, the Hilbert stress-energy tensor $T_{\mu\nu}$ is derived. The independent physical phenomena of an observer -- inertial mass flux, electromagnetic radiation, electroweak Proca mass densities, dilatonic scalar stresses, and gravitational tidal curvature -- emerge naturally as generator-specific projections of the geometry. Weak-field Einstein gravitation ($G_{\mu\nu} = 8\pi G T_{\mu\nu}$) arises without postulating an independent graviton field or external Einstein-Hilbert action. Furthermore, non-linear ($\mathcal{O}(\partial^2)$) terms arise that act to prevent gravitational collapse. Singularities are avoided as a direct condition from the framework. Finally, we show that the theory separates analytically into localized, zero-entropy compacton cores and an ambient, superimposable exterior background medium, establishing the physical foundation for gauge fields and linear quantum wave mechanics prior to operator quantization.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-31
DOI
https://doi.org/10.5281/zenodo.23826078
Primary Topic
Relativity and Gravitational Theory
Type
article
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article

Unification of Gauge Dynamics and Gravitation through Hylodynamics

John RUSNAK
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
article

Unification of Gauge Dynamics and Gravitation through Hylodynamics

John RUSNAK
article en

Abstract

In this paper, we present a pre-metric continuum framework dubbed "Hylodynamics" in which spacetime metricity, Riemannian curvature, and Yang-Mills gauge dynamics emerge concurrently from the non-linear dynamics of s single master field. The fundamental action is strictly first-order in derivatives, defined over an unmetered four-dimensional manifold $M$ with an indefinite-metric spinor space governed by $\mathfrak{icsl}(2, \mathbb{C}) \subset \mathfrak{su}(2,2)$. Spacetime coordinates possess no prior metric, light cones, or volume measure; soldering along the translation generators pulls back the rigid internal the the Minkowski metric onto the coordinates. Spacetime emerges through this soldering and pull-back. Through the Maurer-Cartan connection, the Hilbert stress-energy tensor $T_{\mu\nu}$ is derived. The independent physical phenomena of an observer -- inertial mass flux, electromagnetic radiation, electroweak Proca mass densities, dilatonic scalar stresses, and gravitational tidal curvature -- emerge naturally as generator-specific projections of the geometry. Weak-field Einstein gravitation ($G_{\mu\nu} = 8\pi G T_{\mu\nu}$) arises without postulating an independent graviton field or external Einstein-Hilbert action. Furthermore, non-linear ($\mathcal{O}(\partial^2)$) terms arise that act to prevent gravitational collapse. Singularities are avoided as a direct condition from the framework. Finally, we show that the theory separates analytically into localized, zero-entropy compacton cores and an ambient, superimposable exterior background medium, establishing the physical foundation for gauge fields and linear quantum wave mechanics prior to operator quantization.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 14%
Relativity and Gravitational Theory
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