Weylian reduction theory for self-similar models

yoshikawa, makoto;

A geometrical method of formulating self-similar models in general relativity or in other gravitational theories is presented. The method consists of two techniques: (1) a Kaluza–Klein-like dimensional reduction technique for self-similar spacetimes, and (2) a systematic method of describing tensor fields on a self-similar spacetime in terms of fields on the reduced space. It is shown that the reduced space is aWeyl–Dirac conformal manifold and a self-similar model is formulated as a conformally covariant differential equation system.