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, $$\gamma$$, (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, $$\eta_{\mu\nu}$$:


 * $$g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu} +\mathcal{O}(h^2)$$,

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