## Energy versus Angular Momentum in Black Hole Binaries

by **Damour, Thibault** and **Nagar, Alessandro** and **Pollney, Denis** and **Reisswig, Christian**

4 pages, 2 figures

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 $latex E$ and the (reduced) angular momentum $latex j$ of the system. We show that the relation $latex E(j)$ is an accurate diagnostic of the dynamics of a black-hole binary in a highly relativistic regime. By comparing the numerical-relativity $latex E^{\rm NR} (j)$ curve with the predictions of several analytic approximation schemes, we find that, while the usual, non-resummed post-Newtonian-expanded $latex E^{\rm PN} (j)$ relation exhibits large and growing deviations from $latex E^{\rm NR} (j)$, 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.