TY - JOUR
T1 - The speciality index as invariant indicator in the BKL mixmaster dynamics
AU - Cherubini, C.
AU - Bini, D.
AU - Bruni, Marco
AU - Perjes, Z.
PY - 2005
Y1 - 2005
N2 - The 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
AB - The 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
U2 - 10.1088/0264-9381/22/9/018
DO - 10.1088/0264-9381/22/9/018
M3 - Article
SN - 0264-9381
VL - 22
SP - 1763
EP - 1768
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
IS - 9
ER -