Work

Generalized products and Lorentzian length spaces

Year: 2025

Type: article

Abstract: We construct a Lorentzian length space with an orthogonal splitting on a product $$I\times X$$ I × X of an interval and a metric space and use this framework to consider the relationship between metric and causal geometry, as well as synthetic time-like Ricci curvature bounds. The generalized Lorentzian product carries a natural Lorentzian length structure but can fail the push-up condition in general. We recover the push-up property under a log-Lipschitz condition on the time variable and establish sufficient conditions for global hyperbolicity. Moreover, we formulate time-like Ricci curvature bounds without push-up and regularity assumptions and obtain a partial rigidity of the splitting under a strong energy condition.

Source: Letters in Mathematical Physics

DOI: 10.1007/s11005-025-01910-7

Author: Elefterios Soultanis

Institution: University of Jyväskylä

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990