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

TL;DR

This paper derives the most general exact solution to Einstein's vacuum field equations for diagonal, separable metrics without assuming symmetries, providing a comprehensive analytical framework with arbitrary functions and parameters.

Contribution

It presents the first complete analytical solution for diagonal, vacuum, separable metrics with no symmetry assumptions, including arbitrary functions and explicit parameterization.

Findings

Exact solution with 16 functions reduced to 12 by coordinate choice

Solution includes 3 parameters and 10 constants plus 2 arbitrary functions

No symmetry assumptions; functions separable in space-time variables

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.