Binary-black-hole initial data with nearly extremal spins

Abstract

There is a significant possibility that astrophysical black holes with nearly-extremal spins exist. Numerical simulations of such systems require suitable initial data. In this paper, we examine three methods of constructing binary-black-hole initial data, focusing on their ability to generate black holes with nearly-extremal spins: (i) Bowen-York initial data, including standard puncture data (based on conformal flatness and Bowen-York extrinsic curvature), (ii) standard quasi-equilibrium initial data (based on the extended-conformal-thin-sandwich equations, conformal flatness, and maximal slicing), and (iii) quasi-equilibrium data based on the superposition of Kerr-Schild metrics. We find that the two conformally-flat methods (i) and (ii) perform similarly, with spins up to about 0.99 obtainable at the initial time. However, in an evolution, we expect the spin to quickly relax to a significantly smaller value around 0.93 as the initial geometry relaxes. For quasi-equilibrium superposed Kerr-Schild (SKS) data [method (iii)], we construct initial data with initial spins as large as 0.9997. We evolve SKS data sets with spins of 0.93 and 0.97 and find that the spin drops by only a few parts in 10 4 during the initial relaxation; therefore, we expect that SKS initial data will allow evolutions of binary black holes with relaxed spins above 0.99. Along the way to these conclusions, we also present several secondary results: the power-law coefficients with which the spin of puncture initial data approaches its maximal possible value; approximate analytic solutions for large spin puncture data; embedding diagrams for single spinning black holes in methods (i) and (ii); non-unique solutions for method (ii). All of the initial data sets that we construct contain sub-extremal black holes, and when we are able to push the spin of the excision boundary surface into the super-extremal regime, the excision surface is always enclosed by a second, sub-extremal apparent horizon. The quasilocal spin is measured by using approximate rotational Killing vectors, and the spin is also inferred from the extrema of the intrinsic scalar curvature of the apparent horizon. Both approaches are found to give consistent results, with the approximate-Killing-vector spin showing least variation during the initial relaxation.

Comparing gravitational waveform extrapolation to Cauchy-characteristic extraction in binary black hole simulations

“…[50]. For the spinning, precessing case we use superposed Kerr-Schild data [85]. Both of these methods can produce astrophysically relevant initial data, but the superposed Kerr-Schild method is more flexible and (for example) allows construction of initial data with higher spins [66,85,86].…”

Black-hole–neutron-star mergers at realistic mass ratios: Equation of state and spin orientation effects

“…The residual eccentricities at the end of the iterative procedure are e $ 0:002-0:004. The free variables in the initial data (conformal metric, extrinsic curvature) are the weighted superposition of an isolated black hole in Kerr-Schild coordinates and of an isolated neutron star in isotropic coordinates, following the method developed by Lovelace et al [43] for binary black holes. A more detailed description of the modifications required to apply this method to black-hole-neutron-star systems is given in Foucart et al [40].…”

Initial data for black hole–neutron star binaries: A flexible, high-accuracy spectral method

“…Indeed, the physical volume element on the spatial slice is dV = φ 6 √γ d 3 x, whereγ is the determinant of the conformal metric, and thus R EdV = RẼ d 3 x. The full XCTS system is known to have non-unique solutions for vacuum [33,34]; this may carry over to space-times with matter, but we have not observed non-uniqueness in the course of the present work.…”

“…This choice ensures that close to the BH, the metric is nearly γ KS ij , while away from the hole, we recover conformal flatness and maximal slicing. The introduction of the exponential damping e −(r1/w) 4 is the most important difference between the choices of conformal metric and extrinsic curvature in [33] and [19]. That change is indeed necessary to avoid large deviations from equilibrium.…”

“…Unfortunately, early results from Taniguchi et al [19] have shown that this leads to strong deviations from quasiequilibrium: the difference between the Komar and ADM energies in [19] is of the order of the binding energy. Here, we describe the use of a modification of the Kerr-Schild metric, already applied to BBH by Lovelace et al [33].…”