Mathematical structures of the Universe

by Eckstein, Michał Heller, Michał Szybka, Sebastian J.

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Title Statements

Full title :Mathematical structures of the Universe / edited by Michał Eckstein, Michael Heller, Sebastian J. Szybka.

Edition Statements

Publication Date:2014.

Publication Statements

Publisher(s):Copernicus Center Press
Place of Publication:Kraków
Language:eng
Publication Date:2014.

The Physical Object

Description:1 online resource (457 pages) : : illustrations

Edition Identifiers

ISBN:9788378864714, 8378864715
oclc:on1125224976
LC Classification:QB981
Dewey Decimal:523.1

Intro; Mathematical Structures of the Universe; Table of Contents; Introduction; Part I. General Relativity and Cosmology; Observer dependent geometries; 1. Geometry for observers and observables; 2. Geometry of the clock postulate: Finsler spacetimes; 2.1. De˝nition of Finsler spacetimes; 2.2. Causal structure and observers; 2.3. Dynamics for point masses; 2.4. Observers and observations; 2.5. Field theory; 2.6. Gravity; 3. The local perspective: Cartan geometry of observer space; 3.1. Definition of observer space; 3.2. Introduction to Cartan geometry; 3.3. Cartan geometry of observer space

3.4. Observers and observations3.5. Gravity; 3.6. The role of spacetime; Acknowledgments; References; Classification of classical singularities: a differential spaces approach; 1. Motivation; 2. Fundamental concepts; 3. Spectral properties; 4. B-boundary; 5. Singularities; Acknowledgment; References; The smooth beginning of the Universe; 1. Introduction; 2. Sikorski's di˙erential spaces and GR; 3. A differential space for the flat FRW d-manifold; 4. Time orientability; 5. A smooth evolution with respect to cosmological time; 6. The simplest smoothly evolving models; 7. Interpretation

8. Smoo…