Physics and Initial Data for Multiple Black Hole Spacetimes

TL;DR

This paper investigates the use of conformally Kerr-Schild initial data to estimate the innermost stable circular orbit parameters of black hole binaries, highlighting limitations and spin effects relevant for gravitational wave detection.

Contribution

It presents convergence results and numerical solutions for initial data of black hole binaries using conformally Kerr-Schild metrics, and analyzes their physical content and limitations.

Findings

Newtonian binding energy is present in the superposed Kerr-Schild background.

Initial data approach has deficiencies, especially regarding prior motion and spin-orbital coupling.

Spin-specific effects are observed, aligning with analytical estimates.

Abstract

An orbiting black hole binary will generate strong gravitational radiation signatures, making these binaries important candidates for detection in gravitational wave observatories. The gravitational radiation is characterized by the orbital parameters, including the frequency and separation at the inner-most stable circular orbit (ISCO). One approach to estimating these parameters relies on a sequence of initial data slices that attempt to capture the physics of the inspiral. Using calculations of the binding energy, several authors have estimated the ISCO parameters using initial data constructed with various algorithms. In this paper we examine this problem using conformally Kerr-Schild initial data. We present convergence results for our initial data solutions, and give data from numerical solutions of the constraint equations representing a range of physical configurations. In a first attempt to understand the physical content of the initial data, we find that the Newtonian binding energy is contained in the superposed Kerr-Schild background before the constraints are solved. We examine some deficiencies with the initial data approach to orbiting binaries, especially touching on the effects of prior motion and spin-orbital coupling of the angular momenta. Making rough estimates of these effects, we find that they are not insignificant compared to the binding energy, leaving some doubt of the utility of using initial data to predict ISCO parameters. In computations of specific initial-data configurations we find spin-specific effects that are consistent with analytical estimates.