2012/10/16 by Carla Cederbaum, Cederbaum, Carla
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #gr-qc #math-ph #math.DG #math.MP
paper · pdf · doi:10.48550/arxiv.1210.4436
Conference proceedings "Relativity and Gravitation -- 100 years after Einstein in Prague", 8 pages
arxiv created 2012/10/16 · arxiv updated 2012/10/17
We present a new geometric approach to the study of static isolated general relativistic systems for which we suggest the name geometrostatics. After describing the setup, we introduce localized formulas for the ADM-mass and ADM/CMC-center of mass of geometrostatic systems. We then explain the pseudo-Newtonian character of these formulas and show that they converge to Newtonian mass and center of mass in the Newtonian limit, respectively, using Ehlers' frame theory. Moreover, we present a novel physical interpretation of the level sets of the canonical lapse function and apply it to prove uniqueness results. Finally, we suggest a notion of force on test particles in geometrostatic space-times.