Transverse geometry and physical observers

Details Transverse geometry and physical observers Transverse geometry and physical observers

2007-11-13

arxiv.org/abs/0711.2033v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, no figures

Scientific paper

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.

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