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We perform a statistical analysis of the binary black hole problem in thepost-Newtonian approximation by systematically sampling and evolving theparameter space of initial configurations for quasi-circular inspirals. Througha principal component analysis of spin and orbital angular momentum variableswe systematically look for uncorrelated quantities and find three of them whichare highly conserved in a statistical sense, both as functions of time and withrespect to variations in initial spin orientations. We also look for and findthe variables that account for the largest variations in the problem. Wepresent binary black hole simulations of the full Einstein equations analyzingto what extent these results might carry over to the full theory in theinspiral and merger regimes. Among other applications these results should beuseful both in semi-analytical and numerical building of templates ofgravitational waves for gravitational wave detectors.

Statistical constraints on binary black hole inspiral dynamics