General Relativity, as a Gauge Theory. Singularities

Abstract

Nowadays we understand that it is much more geometrical to lay the “geometry” (and, in particular, the differential geometry) we apply on the functions rather, which are employed in its description, than on an a priori existed “space.” Yet, the former seems to be more akin to the physicists point of view, according to which “geometry, mechanics, and physics form an inseparable theoretical whole”. (See, for instance, S.Y. Auyang [1: p. 144]). Indeed, the functions we alluded to above are essentially the fields, in the physics terminology, hence (see Volume I, Chapt. II), “sections” of appropriate algebra sheaves and/or of their (sheaf) modules, in particular, of what we called throughout the present abstract (sheaf-theoretic) framework the vector sheaves (ibid. Definition 6.1).