Variational Approach to Gravity Field Theories, 1st ed. 2017 From Newton to Einstein and Beyond Undergraduate Lecture Notes in Physics Series

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. Throughoutthe 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.

Part I Introduction.- The character of a scientific theory.- Field Theories and Variational approach.- Fundamental Principles and Field Theories.- Exercises.- Part II Special Relativity.- Motivations.- Mathematical model.- Electromagnetism in SR.- Exercises.- Part III General Relativity.- Motivations.-  Lagrangian formulation of GR.- Applications.- Exercises.- Part IV Beyond Relativity.- Motivations.- Theory and Experiments.- Exercises.

Describes an approach to general relativity particularly relevant for physics students Evidences the continuity, from the point of view of theoretical physics, of all the gravity theories as field theories Presents solved exercises and examples throughout the text Meets the needs of students specializing in theoretical physics and those seeking a better understanding of particular aspects of the subject Includes supplementary material: sn.pub/extras