Energy versus angular momentum in black hole binaries.

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.

Geometry and regularity of moving punctures.

Significant advances in numerical simulations of black-hole binaries have recently been achieved using the puncture method. We examine how and why this method works by evolving a single black hole. The coordinate singularity and hence the geometry at the puncture are found to change during evolution, from representing an asymptotically flat end to being a cylinder.

Recoil velocities from equal-mass binary-black-hole mergers.

The final evolution of a binary-black-hole system gives rise to a recoil velocity if an asymmetry is present in the emitted gravitational radiation. Measurements of this effect for nonspinning binaries with unequal masses have pointed out that kick velocities approximately 175 km/s can be reached for a mass ratio approximately 0.36.

Accurate evolution of orbiting binary black holes.

We present a detailed analysis of binary black hole evolutions in the last orbit and demonstrate consistent and convergent results for the trajectories of the individual bodies. The gauge choice can significantly affect the overall accuracy of the evolution. It is possible to reconcile certain gauge-dependent discrepancies by examining the convergence limit.