# Are numerical relativity solutions actual solutions to the Einstein Field Equations?

Perhaps this requires a more advanced knowledge of differential equations, but are solutions in numerical relativity (for example, the merger of two black holes) actual solutions to the Einstein Field Equations? Or rather, are they approximations to what the Einstein Field Equations would yield? I have generally taken "numerical solution" to mean an approximation to the solution of a differential equation, as in the latter case.

• Do only exact solutions count as “actual” solutions? What if an approximate solution can in principle be made arbitrarily close to exact with enough computational power? – G. Smith Apr 3 '20 at 4:19
• 3.1415 is only an approximation to $\pi$, it is nevertheless very useful for practical purposes – Prof. Legolasov Apr 3 '20 at 7:57