Transverse geometry and physical observers

TL;DR

This paper explores the use of transverse geometry to analyze the spatial structure of cosmological models from the perspective of a physical observer, avoiding traditional foliation methods.

Contribution

It introduces a formalism based on transverse geometry for non-integrable cosmological models, linking it to observer-based spatial analysis without requiring complementary structures.

Findings

Transverse isometries act on spacetime models.

Relationship established between transverse geometry and 1+3 spacetime decompositions.

Framework applicable to non-integrable cosmological models.

Abstract

It is proposed that the mathematical formalism that is most appropriate for the study of spatially non-integrable cosmological models is the transverse geometry of a one-dimensional foliation (congruence) defined by a physical observer. By that means, one can discuss the geometry of space, as viewed by that observer, without the necessity of introducing a complementary sub-bundle to the line bundle of the observer or a codimension-one foliation transverse to the foliation of the observer. The concept of groups of transverse isometries acting on such a spacetime and the relationship of transverse geometry to spacetime threadings (1+3 decompositions) is also discussed.