Indeterministic Quantum Gravity and Cosmology VI. Predynamical Geometry of Spacetime Manifold, Supplementary Conditions for Metric, and CPT

Abstract

This paper is a continuation of the papers [gr-qc/9409010, gr-qc/9505034, gr-qc/9603022, gr-qc/9609035, gr-qc/9609046]. The introduction of a prior, i.e., predynamical global geometry of spacetime manifold is substantiated, and the geometry is specified. The manifold is an infinite four-cylinder, or tube in the five-dimensional Euclidean space, the orthogonal section of the cylinder being the unit three-sphere. Supplementary conditions for metric are introduced geometrically, coordinate-independently, as opposed to coordinate conditions. Parity and time-reversal transformations are extended to the manifold specified. PT is equivalent to a rotation through πabout an axis orthogonal to the cylinder axis. CPT invariance is discussed. Keywords: cosmic time, cosmic space, cylindrical manifold