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

TL;DR

This paper explores the predynamical geometry of spacetime, introducing supplementary conditions for the metric and discussing CPT invariance within a five-dimensional cylindrical manifold framework.

Contribution

It provides a geometric, coordinate-independent formulation of supplementary metric conditions and extends symmetry transformations to a predynamical spacetime manifold.

Findings

Predynamical global geometry of spacetime is substantiated.

Supplementary conditions for the metric are introduced geometrically.

CPT invariance is discussed within the specified manifold.

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 \pi about an axis orthogonal to the cylinder axis. CPT invariance is discussed. Keywords: cosmic time, cosmic space, cylindrical manifold