Approximate Killing Fields as an Eigenvalue Problem

2008/08/12 by Christopher Beetle, Beetle, Christopher
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Pulsars and Gravitational Waves Research #gr-qc

paper · pdf · doi:10.48550/arxiv.0808.1745

4 pages, RevTeX

arxiv created 2008/08/12 · openalex publication_date 2008/08/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Approximate Killing vector fields are expected to help define physically meaningful spins for non-symmetric black holes in general relativity. However, it is not obvious how such fields should be defined geometrically. This paper relates a definition suggested recently by Cook and Whiting to an older proposal by Matzner, which seems to have been overlooked in the recent literature. It also describes how to calculate approximate Killing fields based on these proposals using an efficient scheme that could be of immediate practical use in numerical relativity.

Citations

• Circular orbits and spin in black-hole initial data

Related

• Perturbations of Kerr with approximate Killing spinors -- Part 1: Wave version
• On the local extension of Killing vector-fields in Ricci flat manifolds
• On Killing vector fields and Newman-Penrose constants
• A trick for calculating surface gravities of Killing horizons
• Near-Horizon Symmetries of Local Black Holes in General Relativity