2017/01/01 by Jacques L. Rubin
Mathematics · Physics and Astronomy · #Classical mechanics #Context (archaeology) #Cosmology and Gravitation Theories #Differential geometry #Einstein #General relativity #Mathematics #Mathematics of general relativity #Noncommutative and Quantum Gravity Theories #Numerical relativity #Physics #Projective geometry #Pulsars and Gravitational Waves Research #Pure mathematics #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Spacetime #Spacetime topology #Stationary spacetime #Theoretical physics #Theory of relativity #physics.gen-ph
paper · pdf · doi:10.1155/2017/9672417
published as "Nonperturbative Approaches in Field Theory" (Eds: Ralf Hofmann and Thierry Grandou) of "Advances in High Energy Physics," Volume 2017 (2017), Article ID 9672417 · 28 pages, 16 figures, 12 tables. Work presented at the "5th Winter Workshop on Non-Perturbative Quantum Field Theory," (WWNPQFT) 22-24 March 2017, Institut du Non-Linéaire de Nice, Valbonne (France). http://wwnpqft.inphyni.cnrs.fr/index.html#
openalex publication_date 2017/01/01 · arxiv created 2017/09/04 · arxiv updated 2017/09/05 · openalex created_date 2017/09/15 · openalex updated_date 2026/08/05
Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein’s relativity. Accordingly, a comparison between observational data and theoretical expectations might then be strongly compromised. In the present paper, we give the principles of relativistic localizing systems so as to bypass this issue. Such systems will allow locating users endowed with receivers and, in addition, localizing any spacetime event. These localizing systems are made up of relativistic autolocating positioning subsystems supplemented by an extra satellite. They indicate that spacetime must be supplied everywhere with an unexpected local four-dimensional projective structure besides the well-known three-dimensional relativistic projective one. As a result, the spacetime manifold can be seen as a generalized Cartan space modeled on a four-dimensional real projective space, that is, a spacetime with both a local four-dimensional projective structure and a compatible (pseudo-)Riemannian structure. Localization protocols are presented in detail, while possible applications to astrophysics are also considered.