The Synergy between Numerical and Perturbative Approaches to Black Holes

TL;DR

This paper reviews numerical relativity methods for black hole spacetimes, highlighting the synergy with perturbation theory to improve simulation accuracy and interpret complex black hole interactions.

Contribution

It introduces a combined approach of numerical and perturbative techniques for studying black holes, advancing the understanding of black hole coalescence.

Findings

Progression from axisymmetric to full 3D simulations

Enhanced confidence in simulation results through perturbative methods

Tools developed for interpreting black hole merger simulations

Abstract

I describe approaches to the study of black hole spacetimes via numerical relativity. After a brief review of the basic formalisms and techniques used in numerical black hole simulations, I discuss a series of calculations from axisymmetry to full 3D that can be seen as stepping stones to simulations of the full 3D coalescence of two black holes. In particular, I emphasize the interplay between perturbation theory and numerical simulation that build both confidence in present results and tools to aid and to interpret results of future simulations of black hole coalescence.