Borchers, Hans-Jürgen.
Mathematical Implications of Einstein-Weyl Causality [electronic resource] / by Hans-Jürgen Borchers, Rathindra Nath Sen. - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2006. - XII, 190 p. 37 illus. online resource. - Lecture Notes in Physics, 709 0075-8450 ; . - Lecture Notes in Physics, 709 .
Geometrical Structures on Space-Time -- Light Rays and Light Cones -- Local Structure and Topology -- Homogeneity Properties -- Ordered Spaces and Complete Uniformizability -- Spaces with Complete Light Rays -- Consequences of Order Completeness -- The Cushion Problem -- Related Works -- Concluding Remarks -- Erratum to: Geometrical Structures on Space-Time -- Erratum to: Light Rays and Light Cones -- Erratum to: Local Structure and Topology -- Erratum to: Ordered Spaces and Complete Uniformizability -- Erratum to: Spaces with Complete Light Rays -- Erratum to: Consequences of Order Completeness -- Erratum.
The present work is the first systematic attempt at answering the following fundamental question: what mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The authors propose an axiomatization of Einstein-Weyl causality (inspired by physics), and investigate the topological and uniform structures that it implies. Their final result is that a causal space is densely embedded in one that is locally a differentiable manifold. The mathematical level required of the reader is that of the graduate student in mathematical physics.
9783540376811
10.1007/3-540-37681-X doi
Physics.
Global differential geometry.
Cell aggregation--Mathematics.
Physics.
Theoretical, Mathematical and Computational Physics.
Manifolds and Cell Complexes (incl. Diff.Topology).
Classical and Quantum Gravitation, Relativity Theory.
Differential Geometry.
QC19.2-20.85
530.1
Mathematical Implications of Einstein-Weyl Causality [electronic resource] / by Hans-Jürgen Borchers, Rathindra Nath Sen. - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2006. - XII, 190 p. 37 illus. online resource. - Lecture Notes in Physics, 709 0075-8450 ; . - Lecture Notes in Physics, 709 .
Geometrical Structures on Space-Time -- Light Rays and Light Cones -- Local Structure and Topology -- Homogeneity Properties -- Ordered Spaces and Complete Uniformizability -- Spaces with Complete Light Rays -- Consequences of Order Completeness -- The Cushion Problem -- Related Works -- Concluding Remarks -- Erratum to: Geometrical Structures on Space-Time -- Erratum to: Light Rays and Light Cones -- Erratum to: Local Structure and Topology -- Erratum to: Ordered Spaces and Complete Uniformizability -- Erratum to: Spaces with Complete Light Rays -- Erratum to: Consequences of Order Completeness -- Erratum.
The present work is the first systematic attempt at answering the following fundamental question: what mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The authors propose an axiomatization of Einstein-Weyl causality (inspired by physics), and investigate the topological and uniform structures that it implies. Their final result is that a causal space is densely embedded in one that is locally a differentiable manifold. The mathematical level required of the reader is that of the graduate student in mathematical physics.
9783540376811
10.1007/3-540-37681-X doi
Physics.
Global differential geometry.
Cell aggregation--Mathematics.
Physics.
Theoretical, Mathematical and Computational Physics.
Manifolds and Cell Complexes (incl. Diff.Topology).
Classical and Quantum Gravitation, Relativity Theory.
Differential Geometry.
QC19.2-20.85
530.1