Gravity

This textbook explores approximate solutions to general relativity and their consequences. It offers a unique presentation of Einstein's theory by developing powerful methods that can be applied to astrophysical systems. Beginning with a uniquely thorough treatment of Newtonian gravity, the book develops post-Newtonian and post-Minkowskian approximation methods to obtain weak-field solutions to the Einstein field equations. The book explores the motion of self-gravitating bodies, the physics of gravitational waves, and the impact of radiative losses on gravitating systems. It concludes with a brief overview of alternative theories of gravity. Ideal for graduate courses on general relativity and relativistic astrophysics, the book examines real-life applications, such as planetary motion around the Sun, the timing of binary pulsars, and gravitational waves emitted by binary black holes. Text boxes explore related topics and provide historical context, and over 100 exercises present challenging tests of the material covered in the main text. 'This remarkable book gives a superb pedagogical treatment of topics that are crucial for modern astrophysics and gravitational-wave science, but (sadly) are generally omitted from textbooks on general relativity, or treated much too briefly. With enthusiasm, I recommend this book to all astrophysicists, gravitational physicists, and students of these subjects.' Kip S. Thorne, California Institute of Technology 'This book is likely to become the bedside reading of all students and working scientists interested in Newtonian and Einsteinian gravity. Pedagogically written using fully modern notation, the book contains an extensive description of the post-Newtonian approximation, and is replete with useful results on gravitational waves and the motion of bodies under gravity.' Luc Blanchet, Institut d'Astrophysique de ParisPreface; 1. Foundations of Newtonian gravity; 2. Structure of self-gravitating bodies; 3. Newtonian orbital dynamics; 4. Minkowski spacetime; 5. Curved spacetime; 6. Post-Minkowskian theory: formulation; 7. Post-Minkowskian theory: implementation; 8. Post-Newtonian theory: fundamentals; 9. Post-Newtonian theory: system of isolated bodies; 10. Post-Newtonian celestial mechanics, astrometry and navigation; 11. Gravitational waves; 12. Radiative losses and radiation reaction; 13. Alternative theories of gravity; References; Index.