2025/08/16 by E. Minguzzi, Minguzzi, Ettore · 1 citation
Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · pdf · doi:10.48550/arxiv.2508.11956
openalex publication_date 2025/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
The properties of the stable distance over stable spacetimes are used as a reference to propose a simplified, abstract notion of spacetime. The discussion shows that spacetime, with its topology, causal order and (upper semi-continuous) Lorentzian distance, can be introduced in a general and minimalistic way. Specifically, it is shown that spacetime can be represented as nothing more than a family of functions defined over an arbitrary set, the functions being a posteriori interpreted as rushing time functions. The proof makes use of the product trick which reduces causality and metricity to causality in a space with one additional dimension, so leading to a kind of unification for the notions of time function and proper time. Ultimately, our results show that time fully characterizes spacetime.