121. 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.

122. 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 $\gamma$.

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

Abstract:
Abstract

124. 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.

125. 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.

126. 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