General Exact Solution of Einstein Field Equations for Diagonal, Vacuum, Separable Metrics

Abstract

In this article we find the general, exact solution for the gravitational field equations for diagonal, vacuum, separable metrics. These are metrics each of whose terms can be separated into functions of each space-time variable separately. Other than this, the functions are completely arbitrary; no symmetries are assumed; no limitations are placed on the coordinates. There are 16 functions, which with specific selection of coordinates reduce to 12. Since there are 10 field equations, two functions in the solution are completely arbitrary. The field equations are solved exactly. The solution for each function is presented analytically, with a total of three parameters and ten constants in addition to the two arbitrary functions.