It is shown that observers in the standard ADM $3+1$ treatment of matter are the same as the observers used in the matter treatment of Bondi: they are comoving and local Minkowskian. Bondi’s observers are the basis of the post-quasistatic approximation (PQSA) to study a contracting distribution of matter. This correspondence suggests the possibility of using the PQSA as a test bed for numerical relativity. The treatment of matter by the PQSA and its connection with the ADM $3+1$ treatment are presented, for its practical use as a calibration tool and as a test bed for numerical relativistic hydrodynamic codes.

• Received 2 March 2009

DOI:https://doi.org/10.1103/PhysRevD.79.107502