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| The Newtonian limit of geometrostatics Cederbaum, Carla |
| Haupttitel | The Newtonian limit of geometrostatics |
| Titelvariante | Der Newtonsche Limes der Geometrostatik |
| Autor | Cederbaum, Carla
Geburtsort: Heidelberg |
| Gutachter | Professor Dr. Gerhard Huisken |
| weitere Gutachter | Professor Dr. Jan Metzger |
| Freie Schlagwörter | general relativity; differential geometry; geometric analysis; static metrics; mass; center of mass; Newton |
| DDC | 500 Naturwissenschaften und Mathematik 510 Mathematik 515 Analysis 516 Geometrie 539 Moderne Physik |
| Zusammenfassung | This thesis studies the Newtonian limit of General Relativity (GR). The Newtonian limit can be described as the question if and how the classical Newtonian theory of gravity emerges as a limit of GR when the relevant speeds are small compared to the speed of light. On the one hand, this question is relevant for consistency reasons; on the other hand, it also has practical reasons as the Newtonian theory of gravity is still being used today for astrophysical, astronomical, and technical computations and observations. A deeper understanding of the Newtonian limit can furthermore improve and simplify relativistic modeling, numerical simulations, and physical interpretation. The mathematical study of the Newtonian limit is pursued in the language of frame theory. Frame theory has been suggested in the 1980s by Jürgen Ehlers. It allows for a uniform description of the Newtonian (coordinate variant) and the relativistic (coordinate invariant) theories of gravitation. More specifically, the thesis at hand uses Ehlers' frame theory to analyze the Newtonian limit of physical properties like mass and center of mass of a relativistic system. Its focus lies on the analysis of static isolated relativistic systems whose matter has compact support. For those systems, the author suggests the name ``geometrostatics'' in order to underline the relevance of geometry and to distinguish the theory from the more general theory of geometrodynamics. By establishing suitable analogies to the Newtonian theory of gravitation, the consideration of the Newtonian limit of geometrostatics also leads to a deeper understanding of geometrostatics itself. Tightly connected therewith is the pseudo-Newtonian theory of gravitation which emerges from geometrostatics by a conformal transformation. This theory is particularly useful for studying its Newtonian limit. The pseudo-Newtonian theory moreover helps to imitate many Newtonian concepts within geometrostatics. In this sense, this thesis formulates a second Newtonian law of motion, characterizes equipotential surfaces, and clarifies uniqueness questions concerning geometric and physical properties. In the framework of geometrostatics and the pseudo-Newtonian theory of gravitation, this thesis develops new quasi-local definitions and formulae for the mass and the center of mass of a physical system. Those are related to the asymptotic behavior of the geometrostatic variables as well as to the relativistic asymptotic concepts of mass and center of mass of GR. The new notions differ from the established ones in that they are not only determined asymptotically but already in an immediate neighborhood of the matter. Therefore, they constitute a new tool for the analysis of static systems. At the same time, they enable the author to prove convergence of mass and center of mass in the Newtonian limit. This proof is discussed in the last chapter of this thesis. |
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| Seitenzahl | VI, 125 S. |
| Fachbereich/Einrichtung | FB Mathematik und Informatik |
| Erscheinungsjahr | 2011 |
| Dokumententyp/-Sammlungen | Dissertation |
| Medientyp/Format | Text |
| Sprache | Englisch |
| Rechte | Nutzungsbedingungen |
| Tag der Disputation | 13.07.2011 |
| Erstellt am | 29.07.2011 - 07:55:40 |
| Letzte Änderung | 29.07.2011 - 13:57:04 |
| Statische URL | http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000023871 |
| URN | urn:nbn:de:kobv:188-fudissthesis000000023871-3 |
| Zugriffsstatistik | |
| E-Mail-Adresse | carla.cederbaum@aei.mpg.de |
