Metric for a Temporal Manifold Derived from Special Relativity and Newtonian Classical Gravitational Potential

Abstract

In a previous paper (Austin, 2017) a method for calculating time dilation from Newtonian gravitational potential provided a first order equivalence to Schwarzschild’s solution to Einstein’s field equations. This equivalence is for the transformation of the time component between locations when only the radial component is changed. The derivation from the previous paper will be merged with Special Relativity’s kinetic energy derivation to form a metric for a Riemannian geometry. A geodesic is derived from the metric and compared to Schwarzschild’s solution.