Minkowski space. The spacetime of special relativity. (English) Zbl 1372.83001

Schröter, Joachim

De Gruyter Studies in Mathematical Physics 40. Berlin: De Gruyter (ISBN 978-3-11-048457-1/hbk; 978-3-11-048573-8/ebook). vi, 122 p. (2017).

The present book considers special relativity as a special case of general relativity. This is the logical but not the historical point of view. However, the main parts of the book can be well understood without detailed knowledge of general relativity. On page 55 the author writes: “We formulate the discussion such that it is not only valid for Minkowski space but for any Lorentzian manifold.” Consequently, the author starts already on pages 1 to 7 with notions like “4-dimensional Lorentz \(C^k\) manifold”, “\((0,2)\) tensor field”, “Christoffel symbols” and “semi-Riemannian manifold”. This enables him to introduce special relativity in a form which easily shows its relation to general relativity.
Publisher’s description: In Minkowski-Space the space-time of special relativity is discussed on the basis of fundamental results of space-time theory. This idea has the consequence that the Minkowski-space can be characterized by 5 axioms, which determine its geometrical and kinematical structure completely. In this sense Minkowski-Space is a prolegomenon for the formulation of other branches of special relativity, like mechanics, electrodynamics, thermodynamics etc. But these applications are not subjects of this book.

Reviewer: Hans-Jürgen Schmidt (Potsdam)

MSC:

83-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to relativity and gravitational theory
83A05	Special relativity
53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
00A79	Physics

Keywords:

special relativity; general relativity; 4-dimensional Lorentz manifold; tensor field; Christoffel symbols; semi-Riemannian manifold; axioms