Energy Versus Angular Momentum in Black Hole Binaries

Abstract

Using accurate numerical-relativity simulations of (nonspinning) black-hole binaries with mass ratios 1:1, 2:1, and 3:1, we compute the gauge-invariant relation between the (reduced) binding energy E and the (reduced) angular momentum j of the system. We show that the relation E(j) is an accurate diagnostic of the dynamics of a black-hole binary in a highly relativistic regime. By comparing the numerical-relativity E^(NR)(j) curve with the predictions of several analytic approximation schemes, we find that, while the canonically defined, nonresummed post-Newtonian–expanded E^(PN)(j) relation exhibits large and growing deviations from E^(NR)(j), the prediction of the effective one body formalism, based purely on known analytical results (without any calibration to numerical relativity), agrees strikingly well with the numerical-relativity results.