Approximate Killing Vectors on S^2

TL;DR

This paper introduces a novel method for approximating Killing vectors on S^2 surfaces, outperforming existing techniques, and offers a new tool for analyzing the geometry of distorted black hole horizons.

Contribution

The paper presents a new approach for computing approximate Killing vectors on S^2, improving accuracy when exact solutions do not exist, and applies it to black hole horizon geometry.

Findings

Method yields superior approximations compared to existing methods.

Applicable to studying distorted black hole horizons.

Enhances understanding of horizon geometry in general relativity.

Abstract

We present a new method for computing the best approximation to a Killing vector on closed 2-surfaces that are topologically S^2. When solutions of Killing's equation do not exist, this method is shown to yield results superior to those produced by existing methods. In addition, this method appears to provide a new tool for studying the horizon geometry of distorted black holes.