2012/01/26 by Carla Cederbaum, Cederbaum, Carla · 3 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematics and Applications #Relativity and Gravitational Theory #gr-qc #math.AP #math.DG
paper · pdf · doi:10.48550/arxiv.1201.5433
111 pages, 1 figure, dissertation
arxiv created 2012/01/26 · openalex publication_date 2012/01/26 · arxiv updated 2012/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This thesis discusses the Newtonian limit of General Relativity for static isolated systems with compactly supported matter. We call these systems "geometrostatic" to underline their geometric nature. We introduce new quasi-local notions of mass and center of mass that can be read off locally in the vicinity of the matter/black holes. We prove that these notions asymptotically coincide with ADM-mass and the Huisken-Yau CMC-center of mass. Moreover, we prove that they converge to Newtonian mass and center of mass in the Newtonian limit. The Newtonian limit is discussed in the language of Ehlers' frame theory. Furthermore, we prove several uniqueness claims in geometrostatics as well as other geometric and physical properties of these systems. We analyze equipotential sets, provide a pseudo-Newtonian reformulation of geometrostatics, and prove uniqueness of static photon spheres.