115. J. Gruszczak
Cauchy Boundaries of Space- Times
Int J Theor Phys, vol. 29, pp. 37-43 (1990).

Abstract:
Abstract

116. Andrzej Woszczyna, Andrzej Kułak
Cosmological perturbations - extension of Olson's gauge-invariant method
Class. Quantum Grav., vol. 6, p. 1665 (1989).
[abstract] [journal]

Abstract:
Olson's approach (1976) to gauge-invariant perturbation theory is extended to spatially curved universes. A simple method of generating new gauge-independent quantities is discussed.

117. J. Gruszczak, M. Heller and P. Muitarzynski
Physics With and Without the Equivalence Principle
Foundations of Physics, vol. 19, pp. 607-618 (1989).
[abstract]

Abstract:
A differential manifold (d-manifold, for short) can be defined as a pair (M, C), where M is any set and C is a family of real functions on M which is (i) closed with respect to localization and (ii) closed with respect to superposition with smooth Euclidean functions; one also assumes that (iii) M is locally diffeomorphic to R n. These axioms have a traightforward physical interpretation. Axioms (i) and (ii) formalize certain "compatibility conditions" which usually are supposed to be assumed tacitly by' physicists. Axiom (iii) may be though of as a (nonmetric) version of Einstein's equivalence principle. By dropping axiom (iii), one obtains a more general structure called a differential space (d-space). Every subset of R ~ turns out to be a d-space. Nevertheless it is mathematically a workable structure. It might be expected that somewhere in the neighborhood of the Big Bang there is a domain in which space-time is not a d-manifold but still continues to be a d-space. In such a domain we would have a physics without the (usual form of the) equivalence principle. Simple examples of d-spaces which are not d-manifolds elucidate the principal characteristics the resulting physics would manifest.

118. 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

119. 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.

120. 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.