Variational approach to gravity field theories. From Newton to Einstein and beyond
It is really a hard task to teach Einstein's theory of General Relativity to undergraduates. It is still harder to teach them theories beyond Einstein. But just this is the aim of the present book. And, as far as I can see: It has been successfully fulfilled. Example: Section 7.3. discusses the question which kind of tensors could be used to describe the gravitational field in view of the fact, that masses are positive and attract each other. This excludes vector fields (known from electrodynamics), but allows for scalar fields and rank 2-tensors. Newton's theory is a scalar theory, General Relativity is based on a rank 2-tensor, and so it appears natural to ask for scalar-tensor theories for describing the possible deviations from General Relativity. The book is organized as follows: the ten main chapters have the following topics: 1. Field theory and variational approach, 2. Geometry and physics, 3. Principle of covariance and equivalence principle, 4. Lagrangian approach, 5., 6. and 7. Special Relativity, 8. and 9. General Relativity, and 10. Beyond General Relativity. The four appendices cover together almost 80 pages, there topics are: Calculus of variations, tensor algebra, Special Relativity, and differential geometry. Publisher's description: ``This book offers a detailed and stimulating account of the Lagrangian, or variational, approach to general relativity and beyond. The approach more usually adopted when describing general relativity is to introduce the required concepts of differential geometry and derive the field and geodesic equations from purely geometrical properties. Demonstration of the physical meaning then requires the weak field approximation of these equations to recover their Newtonian counterparts. The potential downside of this approach is that it tends to suit the mathematical mind and requires the physicist to study and work in a completely unfamiliar environment. In contrast, the approach to general relativity described in this book will be especially suited to physics students. After an introduction to field theories and the variational approach, individual sections focus on the variational approach in relation to special relativity, general relativity, and alternative theories of gravity. Throughout the text, solved exercises and examples are presented. The book will meet the needs of both students specializing in theoretical physics and those seeking a better understanding of particular aspects of the subject.''
scientific article; zbMATH DE number 6684810