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arXiv · 1211.6884

A set of invariant quality factors measuring the deviation from the Kerr metric

Alfonso García-Parrado Gómez-Lobo·José M. M. Senovilla
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Abstract

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.

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Alfonso García-Parrado Gómez-Lobo, José M. M. Senovilla. 2013-03-07. A set of invariant quality factors measuring the deviation from the Kerr metric. https://doi.org/10.1007/s10714-013-1518-9

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