Corotating and irrotational binary black holes in quasi-circular orbits

TL;DR

This paper develops a formalism for constructing initial data of binary black holes in quasi-circular orbits, assuming quasi-equilibrium conditions when orbital decay is slow, facilitating more accurate simulations of such systems.

Contribution

The paper introduces a comprehensive set of boundary conditions for initial data of binary black holes in quasi-equilibrium, applicable on apparent horizons and at infinity.

Findings

Formalism enables construction of initial data for quasi-equilibrium black hole binaries.

Boundary conditions are applied on apparent horizons to ensure they are true horizons.

Framework accounts for slow orbital decay, approximating true equilibrium conditions.

Abstract

A complete formalism for constructing initial data representing black-hole binaries in quasi-equilibrium is developed. Radiation reaction prohibits, in general, true equilibrium binary configurations. However, when the timescale for orbital decay is much longer than the orbital period, a binary can be considered to be in quasi-equilibrium. If each black hole is assumed to be in quasi-equilibrium, then a complete set of boundary conditions for all initial data variables can be developed. These boundary conditions are applied on the apparent horizon of each black hole, and in fact force a specified surface to be an apparent horizon. A global assumption of quasi-equilibrium is also used to fix some of the freely specifiable pieces of the initial data and to uniquely fix the asymptotic boundary conditions. This formalism should allow for the construction of completely general quasi-equilibrium black hole binary initial data.