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A set of invariant quality factors measuring the deviation from the Kerr metric. (English) Zbl 1266.83113

Gen. Relativ. Gravitation 45, No. 6, 1095-1127 (2013); erratum ibid.45, No. 6, 1129 (2013).
Summary: 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.

MSC:

83C57 Black holes
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
53Z05 Applications of differential geometry to physics
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)

Software:

xPerm; xAct
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References:

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