We contribute to the subject of the physical interpretation of exact solutions by characterizing them through a systematic study in terms of unambiguous physical concepts coming from systems in linearized gravity. We use the physical meaning of the leading order behavior of the Weyl spinor components $Psi_0^0$, $Psi_1^0$ and $Psi_2^0$ and of the Maxwell spinor components $phi_0^0$ and $phi_1^0$ and integrate from future null infinity inwards the exact field equations. In this way it is assigned an unambiguous physical meaning to exact solutions. We indicate a method to generalize the procedure to radiating spacetimes.