Accurate Evolutions of Orbiting Black-Hole Binaries without Excision

TLDR

The authors introduce a new algorithm for evolving orbiting black‑hole binaries without excision or a corotating shift. The algorithm employs a novel puncture‑conformal‑factor technique within the BSSN formulation, using a precollapsed lapse to keep the evolution nonsingular and stable, and is applied to fully evolve binaries from near the innermost stable circular orbit. The method yields fourth‑order convergent waveforms and accurately computes the radiated energy and angular momentum from the plunge, matching predictions from the Lazarus approach.

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 Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations, when used with a "precollapsed" initial lapse, is nonsingular at the start of the evolution and remains nonsingular 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 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.