Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision

TL;DR

A new algorithm for evolving orbiting black-hole binaries that does not require excision or a corotating shift is presented and fourth-order convergence of waveforms is shown and the radiated gravitational energy and angular momentum from the plunge is computed.

Abstract

We present a new algorithm for evolving orbiting black-hole binaries that does not require excision or a corotating shift. Our algorithm is based on a novel technique to handle the singular puncture conformal factor. This system, based on the BSSN formulation of Einstein's equations, when used with a `pre-collapsed' initial lapse, is non-singular at the start of the evolution, and remains non-singular and stable provided that a good choice is made for the gauge. As a test case, we use this technique to fully evolve orbiting black-hole binaries from near the Innermost Stable Circular Orbit (ISCO) regime. We show fourth order convergence of waveforms and compute the radiated gravitational energy and angular momentum from the plunge. These results are in good agreement with those predicted by the Lazarus approach.

Figures (3)

• Figure 1: The trajectories of the punctures (the circles correspond to positions at t=0, 2.5M, 5M, etc). The common horizon forms just after the puncture complete a half orbit. The punctures continue to orbit throughout the evolution.
• Figure 2: QC0 waveform. The real and imaginary parts of the $(\ell=2, m=2)$ mode of $\psi_4$ calculated at $r=10M$.
• Figure 3: QC0 waveforms. The top plot shows the real part of the $(\ell=2, m=2)$ mode at $r=5M$ for resolutions of $h=M/16, M/24, M/36$. The bottom plot shows the differences between waveforms for $h=M/16$ and $h=M/24$ as well as the difference between waveforms for $h=M/24$ and $h=M/36$. The latter difference has been rescaled by $(3/2)^4$ to demonstrate fourth-order convergence.