February 5, 2008 | M. Campanelli, C. O. Lousto, P. Marronetti, Y. Zlochower
The authors present a novel algorithm for evolving orbiting black-hole binaries without the need for excision or a corotating shift. This algorithm, based on the BSSN formulation of Einstein's equations, uses a 'pre-collapsed' initial lapse to ensure non-singularity at the start of the evolution. The technique is tested by fully evolving orbiting black-hole binaries from near the Innermost Stable Circular Orbit (ISCO) regime, achieving fourth-order convergence of waveforms and accurately computing the radiated gravitational energy and angular momentum. The results are in good agreement with those predicted by the Lazarus approach. The method is designed to handle the singular puncture conformal factor analytically, avoiding coordinate distortions that can kill the run before a common horizon forms. The authors also introduce a 'multiple transition' Fisheye transformation to mitigate the problem of resolving features on different scales in black-hole binary systems. The numerical technique has shown long-term stability and fourth-order convergence up to high resolutions, opening up possibilities for studying more complex astrophysical scenarios.The authors present a novel algorithm for evolving orbiting black-hole binaries without the need for excision or a corotating shift. This algorithm, based on the BSSN formulation of Einstein's equations, uses a 'pre-collapsed' initial lapse to ensure non-singularity at the start of the evolution. The technique is tested by fully evolving orbiting black-hole binaries from near the Innermost Stable Circular Orbit (ISCO) regime, achieving fourth-order convergence of waveforms and accurately computing the radiated gravitational energy and angular momentum. The results are in good agreement with those predicted by the Lazarus approach. The method is designed to handle the singular puncture conformal factor analytically, avoiding coordinate distortions that can kill the run before a common horizon forms. The authors also introduce a 'multiple transition' Fisheye transformation to mitigate the problem of resolving features on different scales in black-hole binary systems. The numerical technique has shown long-term stability and fourth-order convergence up to high resolutions, opening up possibilities for studying more complex astrophysical scenarios.