Features of the gravitational radiation from close hyperbolic encounters of two black holes

Abstract

We numerically investigate the features of gravitational radiation from close, fast hyperbolic encounters of two equal-mass, non-spinning black holes. We analyze angular distributions of the energy flux and its integration in time, and compare them with the predictions by mass-quadrupole calculations applied to the trajectory obtained from numerical simulation. These systems can radiate up to \({\sim }{}10\%\) of their total energy, exceeding the 4–\(5\%\) seen in non-spinning quasi-circular mergers and comparable to the 10–\(11\%\) found in cases with aligned spins. The radiation is predominantly emitted toward the polar region, surpassing the equatorial direction by a factor of 4 to 9. Interestingly, as the impact parameter decreases, the energy allocation ratios toward both directions remain relatively constant and appear to approach the values of quasi-circular binary mergers at the capture threshold. In the orbital plane, the main radiation emerges at positive and negative angles near the asymptote bisector and its symmetric counterpart as generically predicted by the mass-quadrupole approximation. In the stronger-interaction regime with smaller impact parameters, however, the main radiation exhibits a longer duration, a larger angular rotation, and a narrower azimuthal spread, resulting in significant deviations from the mass-quadrupole predictions. In high-velocity encounters, the relativistic beaming effect in the Kovacs-Thorne approximation successfully captures key features of the NR radiation patterns, including the brightening of the secondary radiation profile and the narrowing of the azimuthal spread. The direction-dependent features identified here are valuable not only for exploring the fast and strong regime in general relativity, but also for improving waveform modeling and parameter estimation for hyperbolic encounter signals.