Innermost stable circular orbit of binary black holes

Abstract

We introduce a new method to construct solutions to the constraint equations of general relativity describing binary black holes in quasicircular orbit. Black hole pairs with arbitrary momenta can be constructed with a simple method recently suggested by Brandt and Brügmann, and quasicircular orbits can then be found by locating a minimum in the binding energy along sequences of constant horizon area. This approach produces binary black holes in a "three-sheeted" manifold structure, as opposed to the "two-sheeted" structure in the conformal-imaging approach adopted earlier by Cook. We focus on locating the innermost stable circular orbit and compare with earlier calculations. Our results confirm those of Cook and imply that the underlying manifold structure has a very small effect on the location of the innermost stable circular orbit.

Approximate initial data for binary black holes

“…1 we show E and M as a function of P, including both perturbative and numerical values and their difference. Since the leading order error of the perturbative results scales with 4 P we find remarkably good agreement even for moderately large values of the momentum P. For conformally flat Bowen-York based initial data, P=M 0:6 at the predicted location of the innermost stable circular orbit (ISCO, e.g. [3,4]), at which point the relative error of the perturbative values is approximately 2% for the ADM energy, and less than 1% for the irreducible mass.…”

“…Both deviations scale as P 4 and represent an excess energy over the Schwarzschild value that can be interpreted as being associated with gravitational radiation.…”

“…Most earlier calculations employed the so-called transverse-traceless decomposition of the constraint equations (e.g. [3][4][5][6], see also below), while most more recent calculations solve the constraint equations in the conformal thin-sandwich formalism (e.g. [7][8][9][10]; see also [11][12][13][14] for alternative ways of constructing binary black hole initial data.)…”

“…Some of these calculations [18,19,21] treat the black hole singularity with the so-called puncture method [22] (see also [23,24]). Given that puncture initial data for binary black holes are most easily constructed in the transversetraceless formalism (see [4] and compare [25,26]), this development has renewed some interest in transversetraceless initial data.…”

“…The numerical construction of initial data for binary black holes in quasicircular orbit requires significant computational resources, since it involves stepping through nested iterations of elliptic solves, root-finding and sometimes even minimizations along certain sequences (see [3,4,10] and Sec. III D below).…”