From Relational Source Organization to Schwarzschild Geometry and Geodesics EAS/Scalar Fields — Paper II: Isolated-Source Gravitational Correspondence
- 1Independent Researcher
Abstract
This paper is archived as a speculative research work.
General relativity describes the gravitational field of an isolated spherical source through the Schwarzschild metric and the null and timelike geodesics of that metric. Entanglement-Algebraic Spacetime (EAS), by contrast, begins with reciprocal scalar-bearing relationships and conserved composite loading, without a primitive metric or gravitational force. This paper examines whether a single registered EAS source coefficient can remain consistent through the complete isolated-source gravitational representation: a normalized conditioned-region report, a positive physical mass-length coefficient, radial and tangential spatial curvature, the static vacuum lapse and metric, equivalent areal and isotropic coordinates, and standard geodesic observables. The qualified interface admits a continuous areal-radius source kernel and a tangential-curvature correspondence; the ordinary static vacuum Einstein equations then determine the remaining geometry. Consequently the same conserved source coefficient enters the exact Schwarzschild exterior and its geodesic equations, including light bending, circular null orbits, and timelike orbital stability. The result is a conditional, mathematically explicit source-preservation correspondence. It neither makes the Einstein equations consequences of SF combinatorics alone nor introduces a second SF law for photons, inertial motion, or physical time. Complete calculations and proof conditions are supplied in Sections 2 onward and in the accompanying twelve-theorem mathematical manuscript.
Related
- Nonlinear Multiple-Source Gravity from Conserved Relational Organization EAS/Scalar Fields — Paper III: Finite-Source Gravitational Correspondence
- Correspondence between multileaf topology of closed geodesics and spatiotemporal autocorrelations of hotspot images in Schwarzschild spacetime
- EAS / Scalar Fields: Quantum Gravity: Relational Scale, Conditioned-Region Source Organization, and Qualified Correspondence to General Relativity
- Particle geodesics, shadows and accretion disk luminosity of a Dehnen (1,4,5/2)-Schwarzschild black hole
- Radial quantization of the Schwarzschild geometry: relational observables, evaporation, and remnant state
BibTeX
@misc{labhard2026from,
title = {{From Relational Source Organization to Schwarzschild Geometry and Geodesics EAS/Scalar Fields — Paper II: Isolated-Source Gravitational Correspondence}},
author = {0009-0008-0231-7067 Michael E. Labhard\},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23480650},
url = {https://zenodo.org/records/23480650},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Relational Source Organization to Schwarzschild Geometry and Geodesics EAS/Scalar Fields — Paper II: Isolated-Source Gravitational Correspondence
AU - 0009-0008-0231-7067 Michael E. Labhard\
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23480650
UR - https://zenodo.org/records/23480650
AB - This paper is archived as a speculative research work. General relativity describes the gravitational field of an isolated spherical source through the Schwarzschild metric and the null and timelike geodesics of that metric. Entanglement-Algebraic Spacetime (EAS), by contrast, begins with reciprocal scalar-bearing relationships and conserved composite loading, without a primitive metric or gravitational force. This paper examines whether a single registered EAS source coefficient can remain consistent through the complete isolated-source gravitational representation: a normalized conditioned-region report, a positive physical mass-length coefficient, radial and tangential spatial curvature, the static vacuum lapse and metric, equivalent areal and isotropic coordinates, and standard geodesic observables. The qualified interface admits a continuous areal-radius source kernel and a tangential-curvature correspondence; the ordinary static vacuum Einstein equations then determine the remaining geometry. Consequently the same conserved source coefficient enters the exact Schwarzschild exterior and its geodesic equations, including light bending, circular null orbits, and timelike orbital stability. The result is a conditional, mathematically explicit source-preservation correspondence. It neither makes the Einstein equations consequences of SF combinatorics alone nor introduces a second SF law for photons, inertial motion, or physical time. Complete calculations and proof conditions are supplied in Sections 2 onward and in the accompanying twelve-theorem mathematical manuscript.
ER -