Introduction to 2-spinors in general relativity. (English) Zbl 1021.83001

River Edge, NJ: World Scientific. xii, 191 p. (2003).
This is a text-book on the spinors and 2-spinors within general relativity theory. For pedagogic reasons, the author did not apply the most general approach; e.g., he restricts himself to three space- and one time-dimension even in those circumstances, in which the statements easily generalize to the case of an arbitrary number of spatial directions.
Chapter 1 deals with an unusual view to the Minkowski space-time of special relativity theory: 0’Donnell uses the stereographic projection. In the usual terminology one could say: he applies ideas from projective geometry. This is the easiest way to introduce spinors for special relativity.
With this preparation, the more abstract chapter 2 on the spinor algebra: representation of vectors, including the electromagnetic field, and the Petrov classification of the Weyl tensor in spinor form, got a readable form.
Chapter 3, Spinor Analysis, introduces covariant derivatives, it includes the Geroch-Held-Penrose formalism and the Goldberg-Sachs theorem; and the final chapter 4 deals with the Lanczos spinor.
The appendix presents a 50-pages introduction to general relativity theory; therefore, the book is good reading also for students not being acquainted with that theory. Bibliography and index close this well-written monograph.


83-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to relativity and gravitational theory
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
83A05 Special relativity