High-Energy Collision of Two Black Holes

We study the head-on collision of two highly boosted equal mass, nonrotating black holes. We determine the waveforms, radiated energies, and mode excitation in the center of mass frame for a variety of boosts. For the first time we are able to compare analytic calculations, black-hole perturbation theory, and strong field, nonlinear numerical calculations for this problem. Extrapolation of our results, which include velocities of up to $0.94c$, indicate that in the ultrarelativistic regime about $14\pm 3\%$ of the energy is converted into gravitational waves. This gives rise to a luminosity of order ${10}^{-2}{c}^5/G$, the largest known so far in a black-hole merger.

Figure 1

Dominant multipolar component ${\psi }_{20}(t-r)$ for different values of $\beta$, as indicated in the inset.

Figure 2

Energy spectrum for $l=2$ and different values of $\beta$. Horizontal lines are the corresponding ZFL-PP predictions, vertical lines are the QNM frequencies of the final BH.

Figure 3

Total radiated energy (including error bars) as a function of $\beta$, and best fit using the ZFL prediction.