The Fundamental Gravitational Field (FGF): Axioms, Mathematical Construction and a Stable Wormhole Realization
Abstract
The Fundamental Gravitational Field (FGF) is proposed as a fundamental field that originates with the Big Bang and fills every point of the universe. Its founding hypothesis is a symmetry-breaking pattern: the ground state of the universe is a medium that spontaneously breaks Lorentz boosts (and, where matter is present, spatial translations), and FGF consists of the four Goldstone fields of this breaking, one clock field and three elastic label fields. FGF is thus the medium (“Higgs”) phase of gravity, and the same four fields can exist in different phases, proposed to appear as the dark-energy-like, dark-matter-like, cosmic-web and wormhole faces of a single field. The hypothesis is expressed by six axioms and realized mathematically step by step: chronology protection (Theorem 1), no-go results for a single clock field and for first-derivative clock-plus-solid theories (Theorems 2–5), and a static wormhole stabilized by a momentum-constraint operator, linearly stable from ℓ=0 to ℓ=12 and nonlinearly stable in spherical symmetry. New in this version: the wormhole remains linearly stable with the clock stiffness lowered to the cosmic-web value κ=6×10⁻⁷ and the clock potential lowered to p₂=10⁻⁸ or zero; at nonlinear order the throat is very sensitive to the clock rate, and nonlinear stability is demonstrated for small deformations of the throat. Every claim is labelled [S] speculative, [C] computed, or [L] literature.
This version (v6; FGF working definition 3.1) corrects the nonlinear statement of v5 and supersedes v1–v5.
Related
- Non-A Priori Construction of Time: An A Posteriori Approach to Operational Mathematical Structures, Algebraic Temporal Signatures, and Physical Realization
- Gravitational lensing outside and inside of a marginally unstable photon sphere at a Z2-symmetric wormhole throat in strong deflection limits
- Black hole and wormhole branches in gravitational decoupling
- Exact realization of nonflat Boolean parity costs on Sun trees: Intrinsic recognition and exact construction at treewidth two
- Spectral Realization: Mathematical Principles of Natural Philosophy
BibTeX
@misc{yazan2026fundamental,
title = {{The Fundamental Gravitational Field (FGF): Axioms, Mathematical Construction and a Stable Wormhole Realization}},
author = {Mehmet Ali Yazan},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23602878},
url = {https://zenodo.org/records/23602878},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Fundamental Gravitational Field (FGF): Axioms, Mathematical Construction and a Stable Wormhole Realization
AU - Mehmet Ali Yazan
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23602878
UR - https://zenodo.org/records/23602878
AB - The Fundamental Gravitational Field (FGF) is proposed as a fundamental field that originates with the Big Bang and fills every point of the universe. Its founding hypothesis is a symmetry-breaking pattern: the ground state of the universe is a medium that spontaneously breaks Lorentz boosts (and, where matter is present, spatial translations), and FGF consists of the four Goldstone fields of this breaking, one clock field and three elastic label fields. FGF is thus the medium (“Higgs”) phase of gravity, and the same four fields can exist in different phases, proposed to appear as the dark-energy-like, dark-matter-like, cosmic-web and wormhole faces of a single field. The hypothesis is expressed by six axioms and realized mathematically step by step: chronology protection (Theorem 1), no-go results for a single clock field and for first-derivative clock-plus-solid theories (Theorems 2–5), and a static wormhole stabilized by a momentum-constraint operator, linearly stable from ℓ=0 to ℓ=12 and nonlinearly stable in spherical symmetry. New in this version: the wormhole remains linearly stable with the clock stiffness lowered to the cosmic-web value κ=6×10⁻⁷ and the clock potential lowered to p₂=10⁻⁸ or zero; at nonlinear order the throat is very sensitive to the clock rate, and nonlinear stability is demonstrated for small deformations of the throat. Every claim is labelled [S] speculative, [C] computed, or [L] literature. This version (v6; FGF working definition 3.1) corrects the nonlinear statement of v5 and supersedes v1–v5.
ER -