A set of invariant quality factors measuring the deviation from the Kerr metric |
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Authors: | Alfonso García-Parrado Gómez-Lobo José M M Senovilla |
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Institution: | 1. Centro de Matemática, Universidade do Minho, 4710-057, Braga, Portugal 2. Física Teórica, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain
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Abstract: | A number of scalar invariant characterizations of the Kerr solution are presented. These characterizations come in the form of 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. |
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