2022/10/20 by V. A. Rubakov, Rubakov, V. A., C. Wetterich +1
Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2210.11198
openalex publication_date 2022/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The geometric concept of geodesic completeness depends on the choice of the metric field or "metric frame". We develop a frame-invariant concept of "generalised geodesic completeness" or "time completeness". It is based on the notion of physical time defined by counting oscillations for some physically allowed process. Oscillating solutions of wave functions for particles with varying mass permit the derivation of generalised geodesics and the associated notion of completeness. Time completeness involves aspects of particle physics and is no longer a purely geometric concept.