Higher-dimensional homogeneous cosmological models as autonomous dynamical systems

Details Higher-dimensional homogeneous cosmological models as autonomous dynamical systems Higher-dimensional homogeneous cosmological models as autonomous dynamical systems

Feb 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991gregr..23..189h&link_type=abstract

General Relativity and Gravitation, Volume 23, Issue 2, pp.189-207

Physics

1

Scientific paper

The field equations for homogeneous models in an arbitrary number of dimensions form a Hamiltonian system with constraint forces. Due to the monotonic behavior of the determinant of the induced metric, the evolution of the system can be interpreted as the motion of a particle in an explicitly time-dependent potential. Considering vacuum models, we show that this explicit time-dependence can be eliminated. Using the scaling properties of the Ricci tensor we obtain an autonomous system, for which we can also find a Liapunov function in terms of the n-dimensional Ricci curvature.

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