| _version_ | 1866901237855682560 |
|---|---|
| author | Somazze, Robert William |
| author_facet | Somazze, Robert William |
| contents | <p>This paper introduces and formalizes the theory of Fractal Differential Geometry (FDG), a novel extension to General Relativity (GR) that treats dimensionality as a dynamical scalar field Φ(x). FDG proposes that spacetime dimensionality evolves in response to gravitational fields, resolving classical singularities and yielding observational signatures such as gravitational wave echoes. The framework is anchored by a five-pillar research program—spanning mathematical formulation, dimensional measurement, GR recovery, observational constraints, and quantum embedding. Using numerical integration and observational matching across a spectrum of black hole types (stellar, supermassive, and ultramassive), we confirm that FDG is consistent with GR in classical regimes while providing new predictions near strong gravity. This paper synthesizes the mathematical foundations, empirical validations, and conceptual insights that together establish FDG as a predictive and testable theory of dimensional flow in spacetime.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15669628 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | On Dimensional Flow in Gravitational Spacetime Somazze, Robert William Theoretical physics Black holes <p>This paper introduces and formalizes the theory of Fractal Differential Geometry (FDG), a novel extension to General Relativity (GR) that treats dimensionality as a dynamical scalar field Φ(x). FDG proposes that spacetime dimensionality evolves in response to gravitational fields, resolving classical singularities and yielding observational signatures such as gravitational wave echoes. The framework is anchored by a five-pillar research program—spanning mathematical formulation, dimensional measurement, GR recovery, observational constraints, and quantum embedding. Using numerical integration and observational matching across a spectrum of black hole types (stellar, supermassive, and ultramassive), we confirm that FDG is consistent with GR in classical regimes while providing new predictions near strong gravity. This paper synthesizes the mathematical foundations, empirical validations, and conceptual insights that together establish FDG as a predictive and testable theory of dimensional flow in spacetime.</p> |
| title | On Dimensional Flow in Gravitational Spacetime |
| topic | Theoretical physics Black holes |
| url | https://doi.org/10.5281/zenodo.15669628 |