Non-exact solutions in general relativity are solutions

Solutions of the Einstein field equations

Where appropriate, this article will use the abstract index notation.Solutions of the Einstein field equations are spacetimes that result from solving the Einstein field equations of general relativity. Solving the field equations actually gives Lorentz metrics...

 of Albert Einstein's field equations of general relativity

Einstein field equations

The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...

 which hold only approximately. Common examples are the solutions to the linearized equations which are derived by letting the components g_μν of the metric equal the components η_μν of the flat Minkowski metric plus a small perturbation h_μν, and then dropping all terms which are of second or higher order in h_μν.

See also

• Post-Newtonian expansion
  Post-Newtonian expansion
  Post-Newtonian expansions in general relativity are used for finding an approximate solution of the Einstein equations for the metric tensor. The post-Newtonian approximations are expansions in a small parameter, which is the ratio of the velocity of matter, forming the gravitational field, to the...
  
  
• Parameterized post-Newtonian formalism
  Parameterized post-Newtonian formalism
  Post-Newtonian formalism is a calculational tool that expresses Einstein's equations of gravity in terms of the lowest-order deviations from Newton's theory. This allows approximations to Einstein's equations to be made in the case of weak fields...