Applications of the lichnerowicz Laplacian to stress energy tensors
A generalization of the Laplacian for <em>p</em>-forms to arbitrary tensors due to Lichnerowicz will be applied to a 2-tensor which has physical applications. It is natural to associate a divergencefree symmetric 2-tensor to a critical point of a specific variational problem and it is th...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/10.3934/Math.2017.2.545/fulltext.html |
| _version_ | 1819069260540936192 |
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| author | Paul Bracken |
| author_facet | Paul Bracken |
| author_sort | Paul Bracken |
| collection | DOAJ |
| description | A generalization of the Laplacian for <em>p</em>-forms to arbitrary tensors due to Lichnerowicz will be applied to a 2-tensor which has physical applications. It is natural to associate a divergencefree symmetric 2-tensor to a critical point of a specific variational problem and it is this 2-tensor that is studied. Numerous results are obtained for the stress-energy tensor, such as its divergence and Laplacian. A remarkable integral formula involving a symmetric 2-tensor and a conformal vector field is obtained as well. |
| first_indexed | 2024-12-21T16:47:13Z |
| format | Article |
| id | doaj.art-a1682bf66d304be3a1f3f2d6f4f0a092 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-21T16:47:13Z |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a1682bf66d304be3a1f3f2d6f4f0a0922022-12-21T18:56:57ZengAIMS PressAIMS Mathematics2473-69882017-09-012354555610.3934/Math.2017.2.545Applications of the lichnerowicz Laplacian to stress energy tensorsPaul Bracken0Department of Mathematics, University of Texas, TX 78539-2999 Edinburg, USAA generalization of the Laplacian for <em>p</em>-forms to arbitrary tensors due to Lichnerowicz will be applied to a 2-tensor which has physical applications. It is natural to associate a divergencefree symmetric 2-tensor to a critical point of a specific variational problem and it is this 2-tensor that is studied. Numerous results are obtained for the stress-energy tensor, such as its divergence and Laplacian. A remarkable integral formula involving a symmetric 2-tensor and a conformal vector field is obtained as well.http://www.aimspress.com/article/10.3934/Math.2017.2.545/fulltext.htmlBasis| tensor| connection| differential system| Laplacian| bundle| harmonic map |
| spellingShingle | Paul Bracken Applications of the lichnerowicz Laplacian to stress energy tensors AIMS Mathematics Basis| tensor| connection| differential system| Laplacian| bundle| harmonic map |
| title | Applications of the lichnerowicz Laplacian to stress energy tensors |
| title_full | Applications of the lichnerowicz Laplacian to stress energy tensors |
| title_fullStr | Applications of the lichnerowicz Laplacian to stress energy tensors |
| title_full_unstemmed | Applications of the lichnerowicz Laplacian to stress energy tensors |
| title_short | Applications of the lichnerowicz Laplacian to stress energy tensors |
| title_sort | applications of the lichnerowicz laplacian to stress energy tensors |
| topic | Basis| tensor| connection| differential system| Laplacian| bundle| harmonic map |
| url | http://www.aimspress.com/article/10.3934/Math.2017.2.545/fulltext.html |
| work_keys_str_mv | AT paulbracken applicationsofthelichnerowiczlaplaciantostressenergytensors |