Gravity-dominated unequal-mass black hole collisions

We continue our series of studies of high-energy collisions of black holes investigating unequal-mass, boosted head-on collisions in four dimensions. We show that the fraction of the center-of-mass energy radiated as gravitational waves becomes independent of mass ratio and approximately equal to 13% at large energies. We support this conclusion with calculations using black hole perturbation theory and Smarr’s zero-frequency limit approximation. These results lend strong support to the conjecture that the detailed structure of the colliding objects is irrelevant at high energies.

Figure 1

Convergence plot for a $q=0.10$, $\gamma =1.11$ binary where $v_A=0.87$. The radiated energy is shown in units of the total mass $M$. The inset shows the deviations between coarse, medium, and high resolution rescaled for third-order convergence ($Q_3=1.56$) and fourth-order convergence ($Q_4=1.75$). The dotted curve in the main panel shows the energy extrapolated to infinite resolution using the more conservative third-order estimate.

Figure 2

The dominant multipole ${\psi }_{20}$ of the Newman-Penrose scalar extracted from the most relativistic collisions considered for each mass ratio. The imaginary part of ${\psi }_{20}$ vanishes for all cases due to symmetry.

Figure 3

Total energy radiated $E_{\mathrm{rad}}/M$ as a function of $v_A$.