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Dynamics of inhomogeneities of metric in the vicinity of a singularity in multidimensional cosmology authors

A. A. Kirillov·V. N. Melnikov
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Abstract

The problem of construction of a general ihomogeneous solution of $D$-dimensional Einstein equations in the vicinity of a cosmological singularity is considered. It is shown that near the singularity a local behavior of metric functions is described by a billiard on a space of a constant negative curvature. The billiard is shown to have a finite volume and consequently to be a mixing one. Dynamics of inhomogeneities of metric is studied and it is shown that its statistical properties admit a complete description. An invariant measure describing statistics of inhomogeneities is obtained and a role of a minimally-coupled scalar field in dynamics of the inhomogeneities is also considered.

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A. A. Kirillov, V. N. Melnikov. 1994-08-01. Dynamics of inhomogeneities of metric in the vicinity of a singularity in multidimensional cosmology authors. https://doi.org/10.1103/physrevd.52.723

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