Singularity theorems for warped products and the stability of spatial extra dimensions

Cipriani, Nastassja; Senovilla, José M.M.

doi:10.1007/JHEP04(2019)175

Singularity theorems for warped products and the stability of spatial extra dimensions

Jan 22, 2019

23 pages

Published in:

JHEP 04 (2019) 175

Published: Apr 30, 2019

e-Print:

1901.07271 [gr-qc]

DOI:

10.1007/JHEP04(2019)175

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Abstract: (Springer)

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.

Note:

23 pages, 1 figure. References added, some small rewritting

Spacetime Singularities
Large Extra Dimensions
Cosmology of Theories beyond the SM
higher-dimensional
warped
fibre
singularity
stability
perturbation
space-time

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