Approximate Symmetries in General Relativity
Abstract
Description
The problem of finding an appropriate geometrical/physical index for measuring a degree of inhomogeneity for a given space-time manifold is posed. Interrelations with the problem of understanding the gravitational/informational entropy are pointed out. An approach based on the notion of approximate symmetry is proposed. A number of related results on definitions of approximate symmetries known from literature are briefly reviewed with emphasis on their geometrical/physical content. A definition of a Killing-like symmetry is given and a classification theorem for all possible averaged space-times acquiring Killing-like symmetries upon averaging out a space-time with a homothetic Killing symmetry is proved.
15 pages, LaTeX, extended version (including a review on the subject) of the paper "Approximate Symmetries, Inhomogeneous Spaces and Gravitational Entropy", to appear in Proc. of the Second ICRA Network Workshop "The Chaotic Universe", eds. V. Gurzadyan and R. Ruffini (World Scientific, Singapore, 2000)
15 pages, LaTeX, extended version (including a review on the subject) of the paper "Approximate Symmetries, Inhomogeneous Spaces and Gravitational Entropy", to appear in Proc. of the Second ICRA Network Workshop "The Chaotic Universe", eds. V. Gurzadyan and R. Ruffini (World Scientific, Singapore, 2000)