2015/02/28 by E. Minguzzi · 1 citation
Physics and Astronomy · Mathematics · #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1088/0264-9381/32/18/185008
published as Class. Quantum Grav. 32 (2015) 185008 · 29 pages. v2: expanded treatment of conformal transformations; corrected an error on the conformal transformation of the Ricci scalar
arxiv created 2015/07/21 · arxiv updated 2015/09/25
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain. Indeed, so do the theorems by Hawking, Penrose, Hawking and Penrose, Geroch, Gannon, Tipler, or Kriele, but also the Topological Censorship theorem and so on. It is argued that the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance, geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure, horizons differentiability and conformal transformations are also included.