109. J.Gruszczak, M.Heller
Differential Structure of Space-Time and its Prolongations to Singular Boundary
Int J Theor Phys, vol. 32, pp. 625-648 (1993).

Abstract:
Abstract

110. Andrzej Woszczyna
A dynamical systems approach to the cosmological structure formation - Newtonian universe
Mon. Not. R.A.S., vol. 225, p. 701 (1992).
[journal]

Abstract:
Abstract

111. Andrzej Woszczyna
Gauge invariant cosmic structures : A dynamic systems approach
Phys. Rev. D, vol. 45, pp. 1982-1988 (1992).
[abstract] [journal]

Abstract:
Gravitational instability is expressed in terms of the dynamic systems theory. The gauge-invariant Ellis-Bruni equation and Bardeen's equation are discussed in detail. It is shown that in an open universe filled with matter of constant sound velocity the Jeans criterion does not adequately define the length scale of the gravitational structure.

112. J. Gruszczak, M. Heller, Z. Pogoda
Cauchy Boundaries and b-Incompleteness of Space Times
Int J Theor Phys, vol. 30, pp. 555-565 (1991).

Abstract:
Abstract

113. Leszek M. Sokołowski, Zdzisław A. Golda, Marco Litterio, Luca Amendola
Classical instability of the Einstein-Gauss-Bonnet gravity theory with compactified higher dimensions
Int. J. Mod. Phys. , vol. A6, pp. 4517-4555 (1991).
[abstract] [journal]

Abstract:
The energy spectrum and stability of the effective theory resulting from the Einstein-Gauss-Bonnet gravity theory with compactified internal space are investigated. The internal space can evolve in its volume andór shape, giving rise to a system of scalar fields in the external space-time. The resulting scalar-tensor theory of gravity has physically unacceptable properties. First of all, the scalar fields’ energy is indefinite and unbounded from below, and thereby the gravitational and scalar fields form a self-exciting system. In contradistinction to the case of multidimensional Einstein gravity, this inherent instability of the effective theory cannot be removed by field redefinitions in the process of dimensional reduction (e.g. by a conformal rescaling of the metric in four dimensions, as is done in the former case). To get a viable effective gravity theory one should discard either the geometric scalar fields or the Gauss-Bonnet term from the Lagrangian of the multidimensional theory. It is argued that it is the Gauss-Bonnet term that should be discarded.

114. Marek Demiański, Zdzisław Golda, Waldemar Puszkarz
Dynamics of the D-dimensional FRW-cosmological Models within the Superstring-generated Gravity Model
Gen. Rel. Grav., vol. 23, pp. 917-939 (1991).
[abstract] [journal]

Abstract:
We study the dynamics of the generalized $D$-dimensional ($D = 1 + 3 + d$) Friedman-Robertson-Walker (FRW) cosmological models in the framework of an extended gravity theory obtained by adding the Gauss-Bonnet term to the standard Einstein-Hilbert action. In our discussion we extensively use methods of dynamical systems. We consider models filled in with a perfect fluid obeying the equation of state $p = (\gamma - 1)\rho$ and vacuum but non-flat models. We present a detailed analysis of the ten dimensional model and in particular we study the vacuum case. Several phase portraits show how the evolution of this model depends on the parameter $\gamma$.