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Asymptotic stability of spatially homogeneous spacetimes

1988; IOP Publishing; Volume: 5; Issue: 3 Linguagem: Inglês

10.1088/0264-9381/5/3/008

1361-6382

S. T. C. Siklos,

Advanced Differential Geometry Research

Barrow and Sonoda (1986) have investigated the stability, at large time, of certain Bianchi universes. Their method involves studying a set of first-order differential equations which governs the evolution of the three principal expansion rates, and the conservation equations. This set of equations is not in general equivalent to Einstein's equations; in some cases it may be a subset, or an asymptotic approximation. The results given by Barrow and Sonoda refer to the stability of exact solutions of the Einstein equations with respect to perturbations which are governed by this set of first-order equations, rather than by Einstein's equations. The authors show that the results obtained in this way do not reliably determine whether a spacetime is stable to perturbations which evolve according to the full and exact Einstein equations.