Maximum radiated energy and final spin of high speed collision of two black holes

We performed a series of 769 full numerical simulations of the high-energy collision of black holes to search for the maximum gravitational energy ${E}_{\mathrm{rad}}$ emitted during their merger. We consider equal-mass binaries with spins pointing along their orbital angular momentum $\stackrel{\ensuremath{\rightarrow}}{L}$ and perform a search over impact parameters $b$ and initial linear momenta $p/m=\ensuremath{\gamma}v$ to find the maximum ${E}_{\mathrm{rad}}$ for a given spin $\stackrel{\ensuremath{\rightarrow}}{S}$. The total radiated energy proves to have a weak dependence on the intrinsic spin $s$ of the holes, for the sequence $s=+0.8,0.0,\ensuremath{-}0.8$ studied here. We thus estimate the maximum, ${E}_{\mathrm{rad}}^{\mathrm{max}}/{M}_{\mathrm{ADM}}\ensuremath{\approx}32%\ifmmode\pm\else\textpm\fi{}2%$, for these direct merger encounters. We also explore the radiated angular momentum and the maximum spin of the merger remnant (within these configurations), finding ${\ensuremath{\alpha}}_{f}^{\mathrm{max}}=0.987$. We then use the zero-frequency-limit expansion to analytically model the radiated energy in the small-impact-parameter and large-initial-linear-momentum regime.