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General relativistic quasi-local angular momentum continuity and the stability of strongly elliptic eigenvalue problems
| Title: | General relativistic quasi-local angular momentum continuity and the stability of strongly elliptic eigenvalue problems. |
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| Name(s): |
Wilder, Shawn M., author Beetle, Christopher, Thesis advisor Florida Atlantic University, Degree grantor Charles E. Schmidt College of Science Department of Physics |
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| Type of Resource: | text | |
| Genre: | Electronic Thesis Or Dissertation | |
| Date Created: | 2014 | |
| Date Issued: | 2014 | |
| Publisher: | Florida Atlantic University | |
| Place of Publication: | Boca Raton, Fla. | |
| Physical Form: | application/pdf | |
| Extent: | 87 p. | |
| Language(s): | English | |
| Summary: | In general relativity, angular momentum of the gravitational field in some volume bounded by an axially symmetric sphere is well-defined as a boundary integral. The definition relies on the symmetry generating vector field, a Killing field, of the boundary. When no such symmetry exists, one defines angular momentum using an approximate Killing field. Contained in the literature are various approximations that capture certain properties of metric preserving vector fields. We explore the continuity of an angular momentum definition that employs an approximate Killing field that is an eigenvector of a particular second-order differential operator. We find that the eigenvector varies continuously in Hilbert space under smooth perturbations of a smooth boundary geometry. Furthermore, we find that not only is the approximate Killing field continuous but that the eigenvalue problem which defines it is stable in the sense that all of its eigenvalues and eigenvectors are continuous in Hilbert space. We conclude that the stability follows because the eigenvalue problem is strongly elliptic. Additionally, we provide a practical introduction to the mathematical theory of strongly elliptic operators and generalize the above stability results for a large class of such operators. | |
| Identifier: | FA00004235 (IID) | |
| Degree granted: | Dissertation (Ph.D.)--Florida Atlantic University, 2014. | |
| Collection: | FAU Electronic Theses and Dissertations Collection | |
| Note(s): | Includes bibliography. | |
| Subject(s): |
Boundary element methods Boundary value problems Differential equations, Elliptic -- Numerical solutions Differential equations, Partial -- Numerical solutions Eigenvalues Spectral theory (Mathematics) |
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| Held by: | Florida Atlantic University Libraries | |
| Sublocation: | Digital Library | |
| Persistent Link to This Record: | http://purl.flvc.org/fau/fd/FA00004235 | |
| Use and Reproduction: | Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. | |
| Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
| Host Institution: | FAU | |
| Is Part of Series: | Florida Atlantic University Digital Library Collections. |
