Perturbative stability of the approximate Killing field eigenvalue problem

Abstract

An approximate Killing field may be defined on a compact, Riemannian geometry by solving an eigenvalue problem for a certain elliptic operator. This paper studies the effect of small perturbations in the Riemannian metric on the resulting vector field. It shows that small metric perturbations, as measured using a Sobolev-type supremum norm on the space of Riemannian geometries on a fixed manifold, yield small perturbations in the approximate Killing field, as measured using a Hilbert-type square integral norm. It also discusses applications to the problem of computing the spin of a generic black hole in general relativity.

15 pages

References in corpus (3)

• Binary-black-hole initial data with nearly-extremal spins
• Approximate Killing Vectors on S^2
• Approximate Killing Fields as an Eigenvalue Problem

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• Perturbations of the almost Killing equation and their implications
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