Three-dimensional initial data for the collision of two black holes II: Quasi-circular orbits for equal-mass black holes

TL;DR

This paper develops a method to construct initial data for binary black holes in quasi-circular orbits, determines the innermost stable orbit, and compares results with post-Newtonian approximations, aiding gravitational wave modeling.

Contribution

It introduces an effective-potential approach for initial data construction of binary black holes in quasi-circular orbits, including the innermost stable orbit determination.

Findings

Located the innermost stable quasi-circular orbit for equal-mass nonrotating black holes.

Compared the characteristics of these orbits with previous estimates.

Analyzed the sequence of quasi-circular orbits against post-Newtonian results.

Abstract

The construction of initial-data sets representing binary black-hole configurations in quasi-circular orbits is studied in the context of the conformal-imaging formalism. An effective-potential approach for locating quasi-circular orbits is outlined for the general case of two holes of arbitrary size and with arbitrary spins. Such orbits are explicitly determined for the case of two equal-sized nonrotating holes, and the innermost stable quasi-circular orbit is located. The characteristics of this innermost orbit are compared to previous estimates for it, and the entire sequence of quasi-circular orbits is compared to results from the post-Newtonian approximation. Some aspects of the numerical evolution of such data sets are explored.