Perturbative stability of the approximate Killing field eigenvalue problem
| Autor: | Christopher Beetle, Shawn Wilder |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Physics
Physics and Astronomy (miscellaneous) 010308 nuclear & particles physics General relativity Mathematical analysis FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) Riemannian geometry 01 natural sciences General Relativity and Quantum Cosmology Killing vector field Elliptic operator symbols.namesake Uniform norm Norm (mathematics) 0103 physical sciences symbols Vector field Mathematics::Differential Geometry 010306 general physics Eigenvalues and eigenvectors |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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