121. J. Gruszczak, M. Heller and P. Multtarzynski
A Generalization of Manifolds as Space-Time Model
Journal of Mathematical Physics, vol. 29, pp. 2576-2580 (1988).

Abstract:
Abstract

122. M. Demianski, Z. A. Golda, M. Heller and M. Szydłowski
Kantowski-Sachs multidimensional cosmological models and dynamical dimensional reduction
Class. Quantum Grav., vol. 5, pp. 733-742 (1988).
[abstract] [journal]

Abstract:
Einstein's field equations are solved for a multidimensional spacetime $(KS)\times T^m$, where ($KS$) is a four-dimensional Kantowski-Sachs' spacetime (1966) and $T^m$ is an $m$-dimensional torus. Among all possible vacuum solutions there is a large class of spacetimes in which the macroscopic space expands and the microscopic space contracts to a finite volume. The authors also consider a non-vacuum case and they explicitly solve the field equations for the matter satisfying the Zel'dovich equations of state (1987). In non-vacuum models, with matter satisfying an equation of state $\rho = \gamma\rho$. $0\leq \gamma\leq 1$, at a sufficiently late stage of evolution the microspace always expands and the dynamical dimensional reduction does not occur. Models $(KS)\times B(IX)\times S^1\times S^1\times S^1\times S^1$ and $(KS)\times B(IX)\times B(IX)\times S^1$, where $B(IX)$ is the Bianchi type-$IX$ space, are also briefly discussed. It is shown that there is no chaotic behaviour in these cases. The same conclusion is also valid when one-loop high-temperature quantum corrections generated by a massless scalar field are taken into account.

123. Leszek M. Sokołowski, Zdzisław A. Golda
Instability of Kaluza-Klein cosmology
Phys. Lett., vol. B195, pp. 349-356 (1987).
[abstract] [journal]

Abstract:
We show that cosmological solutions in Kaluza-Klein theory in more than five dimensions are unstable. This is due to the fact that the extra cosmic scale factors appearing in the metric ansatz act as scalar matter fields in the physical four-dimensional spacetime. These fields have physically unacceptable features: their kinetic energy can be negative and the energy spectrum is unbounded from below. To remove the defects a reinterpretation of the cosmological metric ansatz is necessary.

124. M. Biesiada, Z. Golda and M. Szydłowski
On some group properties of Newtonian static star structure equations
J. Phys. A: Math. Gen., vol. 20, pp. 1313-1321 (1987).
[abstract] [journal]

Abstract:
By using Lie group theory, symmetries of the system of equations describing Newtonian static stars in radiative equilibrium are investigated. It turns out that the most general symmetries are those resulting from quasi-homologous transformations. These symmetries enforce a corresponding equation of state. Stromgren's homologous stars are a special case of this, more general, class of solutions.

125. M. Demiański, Z. Golda, L. M. Sokołowski, M. Szydłowski, P. Turkowski
The group-theoretical classification of the 11-dimensional classical homogeneous Kaluza-Klein cosmologies
J. Math. Phys. , vol. 28, pp. 171-173 (1987).
[abstract] [journal]

Abstract:
In the context of the classical Kaluza-Klein cosmology the genalized Bianchi models in 11 dimensions are considered. These are space-times whose spacelike ten-dimensional sections are the hypersurfaces of transitivity for a ten-dimensional isometry group of the total space-time. Such a space-time is a trivial principal fiber bundle $P(M,G_7)$, where $M$ is four-dimensional physical space-time with an isometry group $G_3$ (of a Bianchi type) and $G_7$ is a compact isometry group of the compact isometry group of the compact internal space. The isometry group of $P$ is $G_{10} = G_3 \otimes G_7$, hence all the generalized Bianchi models are classified by enumerating the relevant groups $G_7$. Due to the compactness of $G_7$ the result is astonishingly simple: there are three distinct homogeneous internal spaces in addition to the 11 ordinary Bianchi types for $M$.

126. Zdzislaw A. Golda, Marek Szydlowski, Michal Heller
Generic and nongeneric world models
Gen. Rel. Grav., vol. 19, pp. 707-718 (1987).
[abstract] [journal]

Abstract:
Catastrophe theory methods are employed to obtain a new classification of those world models which can be presented in the form of gradient dynamical systems. Generic sets and structural stability of models in the potential space are strictly defined. It is shown that if a cosmological model is required to be Friedman and generic, it must be flat.