1999/11/01 by Antonio Fernández Rañada · 1 citation
Physics and Astronomy · Mathematics · #Relativity and Gravitational Theory #History and Theory of Mathematics #Mathematics and Applications
paper · doi:10.1088/0143-0807/20/6/503
openalex publication_date 1999/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
General Relativity poses an interesting and exciting challenge for students, not the least part of which is the need for understanding at the same time subtle concepts in physics and in mathematics. The task of the authors is still more enticing, but harder also because of the need to make choices. Some texts concentrate on the former, and others on the latter, while some try to find a balance. This text is an elementary introduction focusing on the mathematical ideas, but without putting an unnecessary emphasis on the formalism. The presentation of the basic ideas of differential geometry is direct, simple and clear. This book has four parts: 1 The Concept of Spacetime; 2 Flat Spacetime and General Relativity; 3 Curved Spacetime and Gravity; and 4 Cosmology. As these titles indicate, the spectrum of the topics is wide and does not omit any fundamental subject at the elementary level. The book is addressed to final-year undergraduate students, although it would be still useful during doctoral studies. It is suitable (and recommended) for studies in both mathematics and in physics. In this latter case, however, it seems appropriate for use in conjunction with other books which may place more emphasis on the physical ideas, for intuitively oriented students. This is evident, for instance, in the pages on energy, fluids or the relation between curvature and gravity. But this last comment must not be taken as a negative appraisal. The author has done a good work. The book is pedagogic and reads easily; I enjoyed the clarity of the text and the fact that it contains a good deal of information at an elementary level in just 217 pages. To sum up, this book is recommended for undergraduate studies both in physics and in mathematics and also for faculty libraries (and for personal collections also in the case of teachers of relativity).