A Solid-Angle Postulate as a Geometric Foundation for Gravity: Escape Velocity and Covariant Formulation in Flat Spacetime
- 1Retired Physicist, Independent Researcher, Baghdad, Iraq
Abstract
We present a geometric foundation for gravity based on a microscopic solid-angle postulate. Each mass element is assumed to exert a gravitational influence on a test mass proportional to the solid angle that the test mass subtends as seen from the element's location. For a spherically symmetric source, direct integration yields the inverse-square law without assuming Newtonian gravity---the 1/r2 behavior emerges purely from geometric dilution. Calibration with Newton's constant gives the Newtonian potential U(r) = −GMm/r. Combining this potential with special-relativistic energy conservation in the source rest frame leads to the exact escape velocity
\[
v_{\text{esc}}(r)=c\sqrt{1-\frac{1}{\bigl(1+GM/(c^{2}r)\bigr)^{2}}}.
\]
The postulate is then extended to a fully covariant, causally consistent formulation in Minkowski spacetime. Using retarded interactions, we obtain for moving point masses the gravitational analogue of the Liénard--Wiechert potential, confirming that the theory respects Lorentz covariance and finite propagation speed c. The resulting scalar theory is formulated entirely in flat spacetime, matches Newtonian gravity in weak fields, and differs from general relativity at order (GM/c2r)2 and higher.
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BibTeX
@misc{farid2026solidangle,
title = {{A Solid-Angle Postulate as a Geometric Foundation for Gravity: Escape Velocity and Covariant Formulation in Flat Spacetime}},
author = {Saad Farid},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23475436},
url = {https://zenodo.org/records/23475436},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Solid-Angle Postulate as a Geometric Foundation for Gravity: Escape Velocity and Covariant Formulation in Flat Spacetime
AU - Saad Farid
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23475436
UR - https://zenodo.org/records/23475436
AB - We present a geometric foundation for gravity based on a microscopic solid-angle postulate. Each mass element is assumed to exert a gravitational influence on a test mass proportional to the solid angle that the test mass subtends as seen from the element's location. For a spherically symmetric source, direct integration yields the inverse-square law without assuming Newtonian gravity---the 1/r^2 behavior emerges purely from geometric dilution. Calibration with Newton's constant gives the Newtonian potential U(r) = −GMm/r. Combining this potential with special-relativistic energy conservation in the source rest frame leads to the exact escape velocity v_esc(r)=c√(1−1/((1+GM/(c^2r))^2)). The postulate is then extended to a fully covariant, causally consistent formulation in Minkowski spacetime. Using retarded interactions, we obtain for moving point masses the gravitational analogue of the Liénard--Wiechert potential, confirming that the theory respects Lorentz covariance and finite propagation speed c. The resulting scalar theory is formulated entirely in flat spacetime, matches Newtonian gravity in weak fields, and differs from general relativity at order (GM/c^2r)^2 and higher.
ER -