General Relativity Sans Differential Geometry: Representing Tensor Elements by Exponential Terms

Precepts of general relativity are derived without using the detailed language of the conventional mathematical approach, differential geometry. Instead, we use the better‐known language of 19th‐century mathematical physics, which was available to Einstein, although he did not use it. This simplifies general relativity derivations, rendering them shorter and easier to follow. As example, we model the precession of the perihelion of Mercury. We also broach the isomorphism between (1) a curved universe with constant in vacuo speed of light, c , and (2) a flat universe with variable c . We draw on this isomorphism to derive the deflection of remote starlight that passes close to the Sun. This considerably shortens the derivation of the solar deflection. The relatively simple alternate approach reported here should be useful to students and teachers of relativity and cosmology at the advanced undergraduate and beginning graduate levels. Also, the perceived hassle of having to construct the full Einstein tensor can be skipped by using it.