Extra-large remnant recoil velocities and spins from near-extremal-Bowen-York-spin black-hole binaries

We evolve equal-mass, equal-spin black-hole binaries with specific spins of $a/m_H\sim 0.925$, the highest spins simulated thus far and nearly the largest possible for Bowen-York black holes, in a set of configurations with the spins counteraligned and pointing in the orbital plane, which maximizes the recoil velocities of the merger remnant, as well as a configuration where the two spins point in the same direction as the orbital angular momentum, which maximizes the orbital hangup effect and remnant spin. The coordinate radii of the individual apparent horizons in these cases are very small and the simulations require very high central resolutions ($h\sim M/320$). We find that these highly spinning holes reach a maximum recoil velocity of $\sim 3300\mathrm{km}{\mathrm{s}}^{-1}$ (the largest simulated so far) and, for the hangup configuration, a remnant spin of $a/m_H\sim 0.922$. These results are consistent with our previous predictions for the maximum recoil velocity of $\sim 4000\mathrm{km}{\mathrm{s}}^{-1}$ and remnant spin; the latter reinforcing the prediction that cosmic censorship is not violated by merging highly spinning black-hole binaries. We also numerically solve the initial data for, and evolve, a single maximal-Bowen-York-spin black hole, and confirm that the 3-metric has an $\mathcal{O}(r^{-2})$ singularity at the puncture, rather than the usual $\mathcal{O}(r^{-4})$ singularity seen for nonmaximal spins.

Figure 1

The ${\gamma }_{xx}$ component of the metric on the initial slice for a single spinning, nonboosted black hole located at the origin with $S=1M^2$ and the puncture mass parameter $m^p=0$. Here we plot ${\gamma }_{xx}$ versus $x$ ($y=z=0.00175M$) and $z$ ($x=y=0.00175M$) and fits to ${\gamma }_{xx}=a+b/(x^2+2c^2)$ (with a similar form for $z$). Note that ${\gamma }_{xx}\propto 1/r^2$ is consistent with the expected $\phi \propto 1/\sqrt{r}$.

Figure 2

The function $u$ for finite $m_p$ in the neighborhood of the puncture. Here the data consists of two BH (the second BH is located at $x/M=-20$ and is not shown). The BH at the origin has spin parameter $S/M^2=1$. Note that $u$ approaches $1/\sqrt{r}$ as $m_p$ tends to zero.

Figure 3

The horizon mass and specific spin for a maximal BY black hole. Here $S=1M^2$ and $m^p=0$. Note that the spin drops rapidly to about $a/m_H=0.934$ (and is still dropping) after the hole absorbs significant mass. The expected asymptotic value is $a/m_H=0.928$.

Figure 4

The specific spins and horizon masses for a binary containing nearly maximal BY spinning holes. The initial spins of the two holes are $a/m_H=0.967$. The individual horizon masses increase rapidly near $t\sim 15M$ as the black holes absorb the spurious radiation. The spin drops to $a/m_H=0.924$ since the spurious radiation does not increase the angular momentum of the holes.

Figure 5

The $xy$ projections of the puncture trajectories for MR0 and MR45, the latter rotated by an angle ${\Theta }_{\mathrm{cor}}$ so that the late inspiral and merger phases overlap.

Figure 6

Recoil velocity versus corrected rotation angle for the MR0-MR315 configurations and a nonlinear least-squares fit to a simple sinusoidal behavior. Note that the corrected rotation angles are not distributed uniformly in the range $(0,2\pi )$.

Figure 7

The puncture trajectories and first common apparent horizon for the MH configuration. Note that the binary completes $\sim 7.5$ orbits prior to merger.

Figure 8

The puncture separation, and first derivative (see inset), versus orbital phase for the MH configuration. Note the decaying oscillations that indicate the ellipticity is significantly reduced after 2 orbits.

Figure 9

The $xy$ projection of the trajectory difference ${\overrightarrow{r}}_1-{\overrightarrow{r}}_2$ for the MH and MR0 configurations. Note the significant hangup effect when the spins are parallel to the orbital angular momentum (MH).

Figure 10

The real part of the ($\ell =2$, $m=2$) mode of ${\psi }_4$ for the MH configuration showing the orbital dynamics and quasinormal decay.