2010/12/20 by Jozef Skákala, Jozef Skakala, Matt Visser · 8 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Causal structure #Class (philosophy) #Combinatorics #Conformal map #Cosmology and Gravitation Theories #Geometry #Isomorphism (crystallography) #Mathematics #Parameterized complexity #Physics #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Quantum field theory in curved spacetime #Quantum mechanics #Spacetime #Stationary spacetime #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/28/6/065007
published in Classical and Quantum Gravity 28(6), 065007 (IOP Publishing) · 8 pages
arxiv created 2010/12/20 · openalex publication_date 2011/02/25 · arxiv updated 2011/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
There is a by now well-established isomorphism between stationary 4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries - these Randers geometries being a particular case of the more general class of 3-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes - the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (time-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.