Evolving the Bowen-York initial data for spinning black holes

TL;DR

This paper investigates the limitations of Bowen-York initial data in accurately modeling spinning black holes by analyzing the radiation emitted during the relaxation to Kerr geometry using second order perturbation theory.

Contribution

It introduces a perturbative approach to quantify the difference between Bowen-York data and true Kerr black holes, highlighting the relaxation effects.

Findings

Quantifies radiation from relaxation of Bowen-York data to Kerr

Uses second order perturbation theory for analysis

Assesses accuracy of Bowen-York data in representing Kerr black holes

Abstract

The Bowen-York initial value data typically used in numerical relativity to represent spinning black hole are not those of a constant-time slice of the Kerr spacetime. If Bowen-York initial data are used for each black hole in a collision, the emitted radiation will be partially due to the ``relaxation'' of the individual holes to Kerr form. We compute this radiation by treating the geometry for a single hole as a perturbation of a Schwarzschild black hole, and by using second order perturbation theory. We discuss the extent to which Bowen-York data can be expected accurately to represent Kerr holes.