2024/08/28 by Tobias Beran, Beran, Tobias, Mathias Braun +13 · 5 citations
Physics and Astronomy · #35J92 #35Q75 #49Q22 #51K10 #53C21 #53C50 (Secondary) #83C75 (Primary) #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2408.15968
openalex publication_date 2024/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The key object is the maximal weak subslope of an arbitrary causal function, which plays the role of the (Lorentzian) modulus of its differential. It is shown to satisfy certain chain and Leibniz rules, certify a locality property, and be compatible with its smooth analog. In this setup, we propose a quadraticity condition termed infinitesimal Minkowskianity, which singles out genuinely Lorentzian structures among Lorentz-Finsler spacetimes. Moreover, we establish a comparison theorem for a nonlinear yet elliptic p-d'Alembertian in a weak form under the timelike measure contraction property. As a particular case, this extends Eschenburg's classical estimate past the timelike cut locus.