Cosmological singularity theorems and splitting theorems for NBakryÉmery spacetimes
We study Lorentzian manifolds with a weight function such that the NBakryÉmery tensor is bounded below. Such spacetimes arise in the physics of scalartensor gravitation theories, including BransDicke theory, theories with KaluzaKlein dimensional reduction, and lowenergy approximations to string theory. In the “pure BakryÉmery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmologicaltype singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite Nvalues N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along futureinextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the NBakryÉmerymore »
 Authors:

^{[1]};
^{[2]}
 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 (Canada)
 215 Carnegie Building, Department of Mathematics, Syracuse University, Syracuse, New York 13244 (United States)
 Publication Date:
 OSTI Identifier:
 22479632
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 2; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BRANES; KALUZAKLEIN THEORY; SINGULARITY; SPACETIME; STRING MODELS; STRING THEORY