A Solid-Angle Postulate as a Geometric Foundation for Gravity: Escape Velocity and Covariant Formulation in Flat Spacetime

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
\[
v_{\text{esc}}(r)=c\sqrt{1-\frac{1}{\bigl(1+GM/(c^{2}r)\bigr)^{2}}}.
\]
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 $(GM/c^{2}r)^{2}$ and higher.