Event Horizons in Numerical Relativity II: Analyzing the Horizon

TL;DR

This paper develops and applies analytical techniques to study the dynamics of event horizons in complex, numerically simulated black hole spacetimes, enhancing understanding of their geometric and physical properties.

Contribution

It introduces new methods for analyzing event horizons, including geometrical measures, generator analysis, and membrane-paradigm quantities, with applications to various black hole scenarios.

Findings

Effective horizon comparison with perturbation theory

Insights into horizon generator behavior

Quantitative analysis of distorted and colliding black holes

Abstract

We present techniques and methods for analyzing the dynamics of event horizons in numerically constructed spacetimes. There are three classes of analytical tools we have investigated. The first class consists of proper geometrical measures of the horizon which allow us comparison with perturbation theory and powerful global theorems. The second class involves the location and study of horizon generators. The third class includes the induced horizon 2-metric in the generator comoving coordinates and a set of membrane-paradigm like quantities. Applications to several distorted, rotating, and colliding black hole spacetimes are provided as examples of these techniques.