Nonextensive Entropy and Geometry in General Relativity

Con-formally invariant metrics can be obtained from the smooth deformation of otherwise flat spacetime. We obtain these metrics from the maximization of the non-extensive entropy of Tsallis with 2nd moments, quadratics of the coordinates as constraints. Evolution equations are Fokker-Planck diffusion type and the usual diffusion tensor (inverse) relations to fundamental metric tensors hold. It is found that an nD deformed q-metric corresponds to an embedding in an (n+1)D flat spacetime, and secondly that a q-non-extensive statistics derived FRW metric and Friedman equations and Hubble term may be obtained and connected to thermo-statistics.