2009/08/07 by Frederic P. Schuller, F. Schüller, Christof Witte +1
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #hep-th
paper · pdf · doi:10.1016/j.aop.2010.04.008
published as Annals Phys.325:1853-1883,2010 · 47 pages, 2 figures
arxiv created 2009/08/07 · openalex publication_date 2010/04/26 · arxiv updated 2011/03/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
Area metric manifolds emerge as a refinement of symplectic and metric geometry in four dimensions, where in numerous situations of physical interest they feature as effective matter backgrounds. In this article, this prompts us to identify those area metric manifolds that qualify as viable spacetime backgrounds in the first place, in so far as they support causally propagating matter. This includes an identification of the timelike future cones and their duals associated to an area metric geometry, and thus paves the ground for a discussion of the related local and global causal structure in standard fashion. In order to provide simple algebraic criteria for an area metric manifold to present a consistent spacetime structure, we develop a complete algebraic classification of area metric tensors up to general transformations of frame. Remarkably, a suitable coarsening of this classification allows to prove a theorem excluding the majority of algebraic classes of area metrics as viable spacetimes.