Approximate Killing Fields as an Eigenvalue Problem

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.

4 pages, RevTeX

References in corpus (5)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Isolated and dynamical horizons and their applications
• Introduction to Isolated Horizons in Numerical Relativity
• Circular orbits and spin in black-hole initial data
• Approximate Killing Vectors on S^2

Cited by in corpus (7)

• Dynamics of marginally trapped surfaces in a binary black hole merger: Growth and approach to equilibrium
• Motion in classical field theories and the foundations of the self-force problem
• Redshift factor and the first law of binary black hole mechanics in numerical simulations
• The spacetime in the neighborhood of a general isolated black hole
• Dynamical Black Holes: Approach to the Final State
• Perturbative stability of the approximate Killing field eigenvalue problem
• Generalized Komar currents for vector fields