Binary-black-hole initial data with nearly-extremal spins

TL;DR

This paper compares methods for constructing initial data of binary black holes with nearly-extremal spins, finding that superposed Kerr-Schild data can achieve initial spins close to 0.9997, enabling more accurate simulations of such systems.

Contribution

It introduces and evaluates a superposition of Kerr-Schild metrics method for initial data, achieving higher initial spins than traditional conformally-flat approaches.

Findings

Conformally-flat methods reach spins up to about 0.99 initially.

Spin relaxes to around 0.93 during evolution with conformally-flat data.

Superposed Kerr-Schild data can start with spins as high as 0.9997, with minimal relaxation.

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 \emph{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. [Abstract abbreviated; full abstract also mentions several secondary results.]