The 3D Grazing Collision of Two Black Holes

TL;DR

For the first time, gravitational waveforms are computed for a grazing collision from a full 3D numerical evolution, and the total energy radiated in gravitational waves is shown to be consistent with the total initial mass of the spacetime and the apparent horizonmass of the final BH.

Abstract

We present results for two colliding black holes (BHs), with angular momentum, spin, and unequal mass. For the first time gravitational waveforms are computed for a grazing collision from a full 3D numerical evolution. The collision can be followed through the merger to form a single BH, and through part of the ringdown period of the final BH. The apparent horizon is tracked and studied, and physical parameters, such as the mass of the final BH, are computed. The total energy radiated in gravitational waves is shown to be consistent with the total mass of the spacetime and the final BH mass. The implication of these simulations for gravitational wave astronomy is discussed.

Figures (7)

• Figure 1: Root-mean-square value of the Hamiltonian constraint on a centered cube with outer boundary at $38m$ and a gridspacing of $0.30m$, $0.24m$, $0.20m$. The curves are rescaled so that they coincide for second order convergence.
• Figure 2: Waveform at resolutions $0.30m$, $0.24m$, $0.20m$.
• Figure 3: Mode $l=m=2$ of the even Zerilli function extracted for different radii as a function of time. A wave that develops after the BHs collide is propagating out.
• Figure 4: A fit to the quasi normal mode determined by $M$ and $a$ shows good agreement in the frequency and decay rate at late times for a resolution of $0.2m$.
• Figure 5: Even and odd wave parts showing differences depending on high, medium, and low-J data.