Gravitation in the fractal D=2 inertial universe: New phenomenology in spiral discs and a theoretical basis for MOND

An interpretation of Mach's Principle led us to consider if it was possible to have a globally inertial universe that was irreducibly associated with a non-trivial global matter distribution, Roscoe (GRG,2002,34,5,577-602, astro-ph/0107397). This question received a positive answer, subject to the condition that the global matter distribution is necessarily fractal, D=2. The purpose of the present paper is to show how general gravitational processes arise in this universe. We illustrate the theory by using it to model an idealized spiral galaxy. One particular subclass of solutions, corresponding to logarithmic spirals, has already been extensively tested in Roscoe A&A,1999,343,788-800 (astro-ph/0107305), and shown to resolve dynamical data over large samples of ORCs with a very high degree of statistical precision. However, this latter analysis led directly to the discovery of a major new phenomenology in spiral discs - that of discrete dynamical classes - comprehensively confirmed in Roscoe A&A,2002,385,431-453 (astro-ph/0107300) over four large independent samples of ORCs. In this paper, we analyse the theory to show how the discrete dynamical classes phenomenology has a ready explanation in terms of an algebraic consistency condition which must necessarily be satisfied. Of equal significance, we apply the theory with complete success to the detailed modelling of a sample of eight Low Surface Brightness spirals (LSBs) which, hitherto, have been succesfully modelled only by Milgrom's MOND algorithm. We are able to conclude that the essence of the MOND algorithm must be contained within the presented theory.Comment: 35 pages, 13 figures. Accepted for publication in GRG (General Relativity and Gravitation