Generating exact solutions to Einstein’s equation using linearized approximations
We show that certain solutions to the linearized Einstein equation can-by the application of a particular type of linearized gauge transformation-be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of...
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| Veröffentlicht in: | Physical review. D 2016-10, Vol.94 (8), Article 084009 |
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| container_title | Physical review. D |
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| creator | Harte, Abraham I. Vines, Justin |
| description | We show that certain solutions to the linearized Einstein equation can-by the application of a particular type of linearized gauge transformation-be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein’s equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations. |
| doi_str_mv | 10.1103/PhysRevD.94.084009 |
| format | Article |
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In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein’s equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations.</description><identifier>ISSN: 2470-0010</identifier><identifier>EISSN: 2470-0029</identifier><identifier>DOI: 10.1103/PhysRevD.94.084009</identifier><language>eng</language><publisher>College Park: American Physical Society</publisher><subject>Eigenvalues ; Eigenvectors ; Einstein equations ; Linearization ; Mathematical analysis ; Plane waves ; Tensors</subject><ispartof>Physical review. 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D</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Harte, Abraham I.</au><au>Vines, Justin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generating exact solutions to Einstein’s equation using linearized approximations</atitle><jtitle>Physical review. D</jtitle><date>2016-10-06</date><risdate>2016</risdate><volume>94</volume><issue>8</issue><artnum>084009</artnum><issn>2470-0010</issn><eissn>2470-0029</eissn><abstract>We show that certain solutions to the linearized Einstein equation can-by the application of a particular type of linearized gauge transformation-be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. 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| fulltext | fulltext |
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| ispartof | Physical review. D, 2016-10, Vol.94 (8), Article 084009 |
| issn | 2470-0010 2470-0029 |
| language | eng |
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| source | American Physical Society Journals |
| subjects | Eigenvalues Eigenvectors Einstein equations Linearization Mathematical analysis Plane waves Tensors |
| title | Generating exact solutions to Einstein’s equation using linearized approximations |
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