El Naschie's Cantorian space-time and general relativity by means of Barbilian's group. A Cantorian fractal axiomatic model of space-time

One builds the vacuum metrics of the stationary electromagnetic field through the complex potential model. There are thus emphasized both a variational principle, independent on the Ricci tensor, and some internal symmetries of the vacuum solutions. One shows that similar results may be obtained using the Barbiliant's group. By analytical continuation of a Barbilian transformation the link between the fixed points of the modular groups of the vacuum and the golden mean Phi = (1/(1 + Phi)) = (root5 - 1)/2 of epsilon((infinity)) space-time is established. Finally, a Cantorian fractal axiomatic model of the space-time is presented. The model is explained using a set of coupled equations which may describe the self organizing processes at the solid-liquid, plasma-plasma, and superconductor-superconductor interfaces. (C) 2003 Elsevier Ltd. All rights reserved.