Non exact solutions in general relativity

Non-exact solutions in general relativity are solutions of Albert Einstein's field equations of general relativity which hold only approximately. These solutions are typically found by treating the gravitational field, g , as a background space-time, γ , (which is usually an exact solution) plus some small perturbation, h . Then one is able to solve the Einstein field equations as a series in h , dropping higher order terms for simplicity.

A common example of this method results in the linearised Einstein field equations. In this case we expand the full space-time metric about the flat Minkowski metric, η μ ν :

and dropping all terms which are of second or higher order in h .