The Post-Quasistatic Approximation as a test bed for Numerical Relativity

TL;DR

The paper demonstrates that the post-quasistatic approximation (PQSA), based on Bondi's observers, can serve as an effective test bed for numerical relativity, linking it with the ADM 3+1 matter treatment.

Contribution

It establishes a correspondence between PQSA and ADM 3+1 observers, proposing PQSA as a calibration and testing tool for numerical relativistic hydrodynamics.

Findings

PQSA aligns with ADM 3+1 matter observers.

PQSA can be used to calibrate numerical relativity codes.

The approach offers a practical test bed for relativistic hydrodynamics simulations.

Abstract

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--quasitatic 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.