Mathematical Implications of Einstein-Weyl Causality

Hans-Jürgen Borchers, Rathindra Nath Sen (auth.)9783540376804, 3540376801

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.

Table of contents :
Introduction….Pages 1-6
Geometrical Structures on Space-Time….Pages 7-14
Light Rays and Light Cones….Pages 15-30
Local Structure and Topology….Pages 31-50
Homogeneity Properties….Pages 51-65
Ordered Spaces and Complete Uniformizability….Pages 67-94
Spaces with Complete Light Rays….Pages 95-101
Consequences of Order Completeness….Pages 103-127
The Cushion Problem….Pages 129-135
Related Works….Pages 137-146
Concluding Remarks….Pages 147-156
Erratum to: Geometrical Structures on Space-Time….Pages 191-191
Erratum to: Light Rays and Light Cones….Pages 191-191
Erratum to: Local Structure and Topology….Pages 191-192
Erratum to: Ordered Spaces and Complete Uniformizability….Pages 192-192
Erratum to: Spaces with Complete Light Rays….Pages 192-192
Erratum to: Consequences of Order Completeness….Pages 192-192
Erratum….Pages 192-192