2007/11/13 by David Delphenich, Delphenich, David
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.0711.2033
23 pages, no figures
arxiv created 2007/11/13 · arxiv updated 2009/12/01
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.