An intuitive and simplified formulation of general relativistic gravity in empty space

Abstract

General relativistic gravity in empty space is formulated using undergraduate calculus, differential equations, and matrix algebra. The key to the formulation involves certain limited assumptions of Newtonian-like behavior in freely falling frames. The formulation results in a field-motion matrix equation that serves essentially the same purpose as Einstein’s field equations in empty space. The limited assumptions of Newtonian-like behavior in freely falling frames are then justified using well-known tensor relationships. To demonstrate its use, the new field-motion equation is used to solve for the Schwarzschild metric.