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Gregory L. Naber - The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity

It is the intention of this book to provide an introduction to the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. In addition to the material on kinematics, particle dynamics and electromagnetic fields that one would expect to find in any introduction to special relativity, the book contains careful treatment of many topics not ordinarily discussed at the elementary level. These include the Reversed Triangle Inequality, Zeeman's Theorem characterizing causal automorphisms as compositions of translations, dilations and orthochronous orthogonal transformations, Penrose's Theorem on the apparent shape of a relativistically moving sphere, the purely algebraic characterization of null and regular electromagnetic fields and an elementary introduction to the theory of spinors. The only prerequisite for this material is a solid course in linear algebra. This book offers a presentation of the special theory of relativity that is mathematically rigorous and treats, in addition to the menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. The treatment presumes only a knowledge of linear algebra and, in two appendices, elementary point-set topology. This new edition includes a chapter on the de Sitter Universe as well as minor updates throughout.

This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman’s characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac’s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. The treatment presumes only a knowledge of linear algebra and, in two appendices, elementary point-set topology.

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