Circular orbits and spin in black-hole initial data

Abstract

The construction of initial data for black-hole binaries usually involves the choice of free parameters that define the spins of the black holes and essentially the eccentricity of the orbit. Such parameters must be chosen carefully to yield initial data with the desired physical properties. In this paper, we examine these choices in detail for the quasiequilibrium method coupled to apparent-horizon/quasiequilibrium boundary conditions. First, we compare two independent criteria for choosing the orbital frequency, the ''Komar-mass condition'' and the ''effective-potential method,'' and find excellent agreement. Second, we implement quasilocal measures of the spin of the individual holes, calibrate these with corotating binaries, and revisit the construction of nonspinning black-hole binaries. Higher-order effects, beyond those considered in earlier work, turn out to be important. Without those, supposedly nonspinning black holes have appreciable quasilocal spin; furthermore, the Komar-mass condition and effective-potential method agree only when these higher-order effects are taken into account. We compute a new sequence of quasicircular orbits for nonspinning black-hole binaries, and determine the innermost stable circular orbit of this sequence.

Approximate Killing vectors onS2

“…Approximate Killing vectors constructed using the KT method are not guaranteed to be divergenceless, although at least in certain cases [4] this can be enforced a posteriori. These approximate Killing vectors also inherit an additional problem.…”

“…As discussed in Ref. [4], the nonspinning black hole data we use are defined by setting the spin measured by the KT method to zero. The corresponding spins measured by our method again differ at most by a few parts in 10 7 , and in all cases we find the value of S ij S ij for the new method to be smaller than the value from the KT solution.…”

“…[4]. We use data for different orbital separations, parameterized by the dimensionless orbital angular velocity M Ω 0 , where M is the total irreducible mass of the binary.…”

“…(1). In some cases, conformal Killing vectors have been used, and have yielded physically reasonable results [4]. Better still, a "Killing Transport" (KT) technique [5], which finds exact Killing vectors when they are present, has been recently adopted, and appears to give physically reasonable results (cf Refs.…”

“…Better still, a "Killing Transport" (KT) technique [5], which finds exact Killing vectors when they are present, has been recently adopted, and appears to give physically reasonable results (cf Refs. [4,6]). Our definition is shown to be even better in a well-defined least squared sense and, for coalescing binary black holes, yields other interesting results worthy of further investigation.…”