A set of invariant quality factors measuring the deviation from the Kerr metric
| Autor: | Gómez-Lobo, Alfonso García-Parrado, Senovilla, José M. M. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10714-013-1518-9 |
| Popis: | A number of scalar invariant characterizations of the Kerr solution are presented. These characterizations come in the form of {\em quality factors} defined in stationary space-times. A quality factor is a scalar quantity varying in the interval $[0,1]$ with the value 1 being attained if and only if the space-time is locally isometric to the Kerr solution. No knowledge of the Kerr solution is required to compute these quality factors. A number of different possibilities arise depending on whether the space-time is Ricci-flat and asymptotically flat, just Ricci-flat, or Ricci non-flat. In each situation a number of quality factors are constructed and analysed. The relevance of these quality factors is clear in any situation where one seeks a rigorous formulation of the statement that a space-time is "close" to the Kerr solution, such as: its non-linear stability problem, the asymptotic settlement of a radiating isolated system undergoing gravitational collapse, or in the formulation of some uniqueness results. Comment: 34 pages, 6 figures. References added, acknowledgments section expanded. Presentation improved and role of the Killing vector change of scale clarified. To appear in General Relativity and Gravitation |
| Databáze: | arXiv |
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