Christian Cherubini et al 2005 Class. Quantum Grav. 22 1763 doi:10.1088/0264-9381/22/9/018
Christian Cherubini1,2,3, Donato Bini2,4,5, Marco Bruni3 and Zoltan Perjes6
Show affiliationsThe long-standing difficulty in general relativity of classifying the dynamics of cosmological models, e.g. as chaotic, is directly related to the gauge freedom intrinsic to relativistic spacetime theories: in general the invariance under diffeomorphisms makes any analysis of dynamical evolution dependent on the particular choice of time slicing one uses. We show here that the speciality index, a scalar dimensionless curvature invariant that has been mainly used in numerical relativity as an indicator of the special or non-special Petrov-type character of a spacetime, is a time-independent quantity (a pure number) at each Kasner step of the Belinski–Khalatnikov–Lifshitz (BKL) map approximating the mixmaster cosmology. Thus the BKL dynamics can be characterized in terms of the speciality index, i.e. in terms of curvature invariants directly related to observables. Possible applications for the associated mixmaster dynamics are discussed.
04.20.-q Classical general relativity
83C25 Approximation procedures, weak fields
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 9 (7 May 2005)
Received 13 August 2004, in final form 11 February 2005
Published 12 April 2005
Christian Cherubini et al 2005 Class. Quantum Grav. 22 1763
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