2008/10/08 by Bogdan G. Dimitrov, Dimitrov, Bogdan G.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #hep-th
paper · pdf · doi:10.48550/arxiv.0810.1503
21 pages; this is a part of the former hep-th/0511136, but with a new "Discussion" part and also Appendices A and B; also minor corrections and changes in the text and in the enumeration of the formulaes; subm. to Gen. Rel. Grav
arxiv created 2008/10/08 · openalex publication_date 2008/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this second part of the paper, dedicated to theories with extra dimensions, a new physical notion about the "tensor length scale" is introduced, based on the gravitational theories with covariant and contravariant metric tensor components. Then the notion of "compactification" in low energy type I string theory is supplemented by the operation of "rescaling" of the contravariant metric components. For both the cases of "rescaling + compactification" and "compactification + rescaling", quasilinear differential equations in partial derivatives have been obtained and the corresponding solutions have been found for the scale (length) function and for the case of a flat 4D Minkowski space, embedded into a 5D space with an exponential warp factor. A differential equation has been obtained and investigated also from the equality of the "rescaled" scalar curvature with the usual one.