Spacetime, geometry and gravitation
This is an introductory book on the general theory of relativity, partly composed in a quite individual style. It is divided into three parts, where each of them could be taken as an independent text. The first part is a preliminary course on general relativity with minimum preparation, starting from a discussion of some features of Newtonian mechanics and Maxwell's electrodynamics, continuing with a consideration of Gauss' work on the geometry of two-dimensional surfaces to introduce the concept of curvature, and ending with basics of general relativity without already saying what the words ``tensor'', ``connection'' etc. geometrically mean. The second part builds the mathematical background of general relativity. It is an introduction to Riemannian geometry containing more mathematics than strictly required for Part III. The third part is a more extensive representation of topics of general relativity. It includes discourses about the energy-momentum tensor of a fluid and the derivation of Einstein's equations from an action principle, and it discusses topics like static and stationary space-times, Fermi-Walker transport, Penrose diagrams, the Schwarzschild and Kerr metrics, and the weak-field approximation of general relativity (followed by the calculation of gravitomagnetic effects and gravitational waves). The book ends with two brief sections on relativistic standard cosmology and the Gauss-Codazzi and the Raychaudhuri equations. It should be mentioned that there are some small deficiencies of this representation. For instance, the author speaks explicitly of the Newton, but only implicitly of the Einstein principle of equivalence, a fact that weakens his arguments in favor of the need of the transition to a curved Riemannian space-time. Or, in two elucidating sections, he extensively explains the structure of the energy-momentum tensor of a fluid as source term in Einstein's equations. But, two sections later, when he discusses electrodynamics it is not mentioned that electrodynamic and other matter fields possess an energy-momentum tensor, too, by which they are also sources of gravitation. However, except for such rare cases, this book is a compendium of general relativity that is really useful to students, not least since each chapter is closed by a tutorial containing exercises and their solutions.
scientific article; zbMATH DE number 5530238