2017/07/25 by Olivier Brunet, Brunet, Olivier
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Mathematics and Applications #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1707.07942
openalex publication_date 2017/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Considering an extension of the principle of covarience to the action along a path in relativistic Lagrangian mechanics, we motivate the use of geometric -- i.e. covariant and parameter invariant -- Lagrangian functions. We then study some properties of geometric Lagrangians, and introduce the notion of deviation of a path, which is a covariant measure of how much a path departs from a geodesic. Finally, we apply this notion of the twin paradox, and provide a rigorous resolution of it.