Accurate Evolutions of Orbiting Black-Hole Binaries without Excision

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 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 (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.PACS numbers: 04.25. Dm, 04.25.Nx, 04.30.Db, 04.70.Bw One of the most significant goals of numerical relativity is to compute accurate gravitational waveforms from astrophysically realistic simulations of merging black-hole binaries. The expectation of very strong gravitational wave emission from the merger of two black holes, and some of the newest astrophysical observations, from supermassive galactic nuclei just about to merge [1] to stellar size black-hole binaries, make these systems one of the most extraordinary astrophysical objects under study today. Binary black hole mergers are expected not only to provide information about the history and formation of the binary system but also to provide important precise tests of strong-field, highly dynamical relativity.Motivated by the forthcoming observations of groundbased gravitational wave detectors, such as LIGO [2], and by the next generation of space-based detectors, such as LISA [3], the numerical relativity community has dedicated a great deal of effort to solving the binary-blackhole problem over the past few decades. After the 'Binary Black Hole Grand Challenge' [4] several new approaches have been pursued in the attempt to produce stable three-dimensional (3D) numerical codes capable of evolving the full Einstein field equations in the absence of any symmetry. This includes the introduction of new formulations of these equations and the development of numerical techniques for accurate evolutions of black-hole binaries, such as higher order finite differencing, spectral methods, and adaptive mesh refinement (AMR) (see Ref.[5] and references therein).The calculation of the gravitational radiation emitted from plunging black-hole binaries was pioneered through the use of the Lazarus approach, which bridges numerical relativity and perturbative techniques to extract approximate gravitational waveforms [6,7,8]. More recently important progress has been made toward evolving orbiting binary-black-hole spacetimes with the use of stable full 3D numerical relativity codes using corotating gauge conditions and singularity excision [9,10,11].Here we present a novel technique for evolving orbiting black holes based on puncture data. This technique does not ...

Post-Newtonian templates for binary black-hole inspirals: the effect of the horizon fluxes and the secular change in the black-hole masses and spins

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