Complexity in spacetime and gravitation - I. From chaos to superchaos

We intend to show in this paper that the two fundamental concepts of the 'Grand Unification' and the 'Chaos Theory' are essential constituent elements of a 'theory of everything' and appertain, in fact, to the overall domain of complexity in space, time and gravitation. The authors hope that the present paper may offer suggestions for the necessary methodology in the analysis of complex problems. Following a short review of the main concepts describing conventional complexity, we introduce as an example of a possible development in standard paradigms, a new type of Rayleigh-Benard instability which may be generated in the interior of a gravitating body and may be the cause of earthquake phenomena. We define the new terminologies of constructive and destructive resonances es in relation to the stability of the solar system. We attempt to find a physical argument in support of the invariant character of a gravitational chaos. Within the frame of a Riemannian spacetime we obtain also a mathematical formulation of El Naschie's conjecture: gravity is caused by an average deviation of fractal time from linear uniform time. We study also in some detail the physics of black holes because black holes offer perfect laboratories for all manifestations of complexities and simplicites. We stress that singularities as well as chaos demonstrate an invariant character. Even the Schwarzschild radius, which was initially considered to be merely a coordinate singularity, is found to retain or deepen its physical significance by diffeomorphisms. Symmetry principles in particle physics and continuous attempts to find a fundamental and unique constituent (strings, p-branes, etc.) of matter are reviewed and their link with complexity, dimensionality of spacetime and chaos is indicated. Particular attention is paid to spontaneous symmetry breaking and the Higgs mechanism in the context of a cascade of concepts: classical lattice gas, Ising, model, order-disorder transition, inflationary scenario, and the universe as a lattice. This cascade tends to confirm the universality of the lattice structure of the universe. In the final section of this first part of the paper we propose a novel multi-spherical cosmic fractal as a model of homogeneous and isotropic cosmologies. If chaos is generated at the level of a background-arena in spacetime, then additional chaotic manifestations generated in this arena represent chaos on a higher level or scale. The suggestion is offered that a chaos on a higher level called 'superchaos' interlaces with chaotic effects at different lower levels. The two other prospective parts of the paper will refer to the subjects: Part 2. Chaoticity of Anisotropic Cosmologies. Part 3. Elementary Particles, Dark Matter and Information Aspects in Relativity. (C) 1998 Elsevier Science Ltd. All rights reserved.