Introduction to Tensor Calculus, Relativity and Cosmology

Rating:
Summary: The easiest and the cheapest technical introduction to GR
Review: There are many books on General Relativity but the reader has to be careful to pick the right one so as not to waste his (or rarely her) time and money! Lawden's book belongs to the class of technical introductions - it requires you to have an undergraduate background in physics and mathematics. The author is primarily a teacher and he has taken care to make the material as easy to understand as possible. On the other hand, this book will not enable you to go directly to the research literature. A great plus of the book is the very reasonable price. I have had the infuriating experience of paying more than $100 for a highly praised textbook only to find it unreadable. The mathematical formalism Lawden employs (tensor calculus based on covariant and contravariant tensors) is now considered old fashioned but it is still the easiest for a beginner in my opinion. Once you have finished this book, I recommend that you read Synge and Schild's "Tensor Calculus" for more depth in the mathematics and also "The Principle of Relativity" (a collection of original papers by Einstein and others) to get a feeling for the history of the subject. Both of these are also Dover paperbacks and very cheap. Then if you want a more modern approach, I recommend Schutz's "A First Course in General Relativity" which is still reasonably priced and will bring you closer to the level of contemporary research. Schutz uses a formalism of tensor calculus which aligns it with differential geometry and is now used in advanced textbooks.