Statistical constraints on binary black hole inspiral dynamics

TL;DR

This paper statistically analyzes binary black hole inspiral dynamics using post-Newtonian approximation, identifying conserved quantities and variables accounting for variations, with implications for gravitational wave modeling.

Contribution

It introduces a systematic statistical approach to identify conserved and variable parameters in binary black hole inspirals, bridging post-Newtonian and full Einstein simulations.

Findings

Identified three highly conserved quantities in a statistical sense.

Found variables that explain the largest variations in the inspiral dynamics.

Demonstrated potential applicability to gravitational wave template construction.

Abstract

We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal component analysis of spin and orbital angular momentum variables we systematically look for uncorrelated quantities and find three of them which are highly conserved in a statistical sense, both as functions of time and with respect to variations in initial spin orientations. We also look for and find the variables that account for the largest variations in the problem. We present binary black hole simulations of the full Einstein equations analyzing to what extent these results might carry over to the full theory in the inspiral and merger regimes. Among other applications these results should be useful both in semi-analytical and numerical building of templates of gravitational waves for gravitational wave detectors.