Borchers H., Sen R.N. Mathematical Implications of Einstein-Weyl Causality

Springer-Verlag Berlin Heidelberg, 2006. — 190 p. — (Lecture Notes in Physics 709). — ISBN: 978-3-540-37681-1 (eBook), 978-3-642-07233-8 (Softcover), 978-3-540-37680-4 (Hardcover).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.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: Local Structure and Topology.
Erratum to: Geometrical Structures on Space-Time.
Erratum to: Light Rays and Light Cones.
Erratum to: Consequences of Order Completeness.
Erratum to: Spaces with Complete Light Rays.
Erratum to: Ordered Spaces and Complete Uniformizability.
Erratum.