Parameter matching between Post-Newtonian and Numerical Relativity in binary black hole systems

We examine the differences between parameter definitions in Post-Newtonian (PN) theory and Numerical Relativity (NR) simulations of binary black hole systems. NR parameters are measured quasi-locally on the apparent horizon, whereas PN parameters are attributed to point particles through asymptotic matching in "body zones". While these discrepancies are expected to be small and diminish at infinite separation, they are not negligible at finite distances. By solving for the apparent horizon in black hole perturbation theory and performing asymptotic matching with the PN metric, we establish the relationship between PN and NR parameter definitions. This parameter matching is crucial for hybridizing PN and NR waveforms and for providing better initial conditions in NR and Cauchy-Characteristic Evolution (CCE) simulations.