Einstein's first gravitational field equation 101 years latter
We review and strengthen the arguments given by Einstein to derive his first gravitational field equation for static fields and show that, although it was ultimately rejected, it follows from General Relativity (GR) for negligible pressure. Using this equation and considerations folowing directly from the equivalence principle (EP), we show how Schwarzschild metric and other vacum metrics can be obtained immediately. With this results and some basic principles, we obtain the metric in the general spherically symmetric case and the corresponding hydrostatic equilibrium equation. For this metrics we obtain the motion equations in a simple and exact manner that clearly shows the three sources of difference (implied by various aspects of the EP) with respect to the Newtonian case and use them to study the classical tests of GR. We comment on the origin of the problems of Einstein first theory of gravity and discuss how, by removing it the theory could be made consistent and extended to include rotations, we also comments on various conceptual issues of GR as the origin of the gravitational effect of pressure.