2019/01/31 by Nastassja Cipriani, José M. M. Senovilla
Mathematics · Physics and Astronomy · #Base (topology) #Black Holes and Theoretical Physics #Extra dimensions #Function (biology) #Geodesic #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Image warping #Product (mathematics) #Singularity #Stability (learning theory) #gr-qc #hep-th #math-ph #math.DG #math.MP
paper · pdf · doi:10.1007/jhep04(2019)175
23 pages, 1 figure. References added, some small rewritting
openalex created_date 2019/02/21 · arxiv created 2019/04/01 · openalex publication_date 2019/04/01 · arxiv updated 2019/05/22 · openalex updated_date 2026/08/05
A bstract New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the warped product is assumed to be our visible 4-dimensional world, while the extra dimensions define the fiber, hence we consider extra-dimensional evolution . Explicit conditions on the warping function that lead to geodesic incompleteness are given. These conditions can be appropriately rewritten, given a warping function, as restrictions on the intrinsic geometry of the fiber — i.e. the extra dimensional space. To find the results, the conditions for parallel transportation in warped products in terms of their projections onto the base and the fibers have been solved, a result of independent mathematical interest that has been placed on an appendix.