Close limit evolution of Kerr-Schild type initial data for binary black holes

TL;DR

This paper develops a method to evolve close-limit binary black hole initial data of Kerr-Schild type, providing insights into gravitational wave emission during black hole mergers.

Contribution

It introduces an exact solution for linearized evolution of Kerr-Schild initial data and clarifies parameter meanings through radiated energy and waveform analysis.

Findings

Derived an exact linearized solution for close-limit black hole initial data

Analyzed gravitational waveforms and energy radiated during black hole collisions

Enhanced understanding of initial data parameters in black hole merger simulations

Abstract

We evolve the binary black hole initial data family proposed by Bishop {\em et al.} in the limit in which the black holes are close to each other. We present an exact solution of the linearized initial value problem based on their proposal and make use of a recently introduced generalized formalism for studying perturbations of Schwarzschild black holes in arbitrary coordinates to perform the evolution. We clarify the meaning of the free parameters of the initial data family through the results for the radiated energy and waveforms from the black hole collision.