Newtonian, post-Newtonian, Relativistic

Eric Poisson and Clifford M. Will

Honorable mention, Textbook/Physical Sciences and Mathematics, 2015 PROSE Awards

(The American Publishers Awards for Professional and Scholarly Excellence)

This textbook, published by Cambridge University Press, 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 Paris


  1. Foundations of Newtonian gravity

    1. Newtonian gravity. 2. Equations of Newtonian gravity. 3. Newtonian field equations. 4. Equations of hydrodynamics. 5. Spherical and nearly spherical bodies. 6. Motion of extended fluid bodies. 7. Bibliographical notes. 8. Exercises.

  2. Structure of self-gravitating bodies

    1. Equations of internal structure. 2. Equilibrium structure of spherical bodies. 3. Rotating self-gravitating bodies. 4. General theory of deformed bodies. 5. Tidally deformed bodies. 6. Bibliographical notes. 7. Exercises.

  3. Newtonian orbital dynamics

    1. Celestial mechanics from Newton to Einstein. 2. Two bodies: Kepler's problem. 3. Perturbed Kepler problem. 4. Case studies of perturbed Keplerian motion. 5. More bodies. 6. Lagrangian formulation of Newtonian dynamics. 7. Bibliographical notes. 8. Exercises.

  4. Minkowski spacetime

    1. Spacetime. 2. Relativistic hydrodynamics. 3. Electrodynamics. 4. Point particles in spacetime. 5. Bibliographical notes. 6. Exercises.

  5. Curved spacetime

    1. Gravitation as curved spacetime. 2. Mathematics of curved spacetime. 3. Physics in curved spacetime. 4. Einstein field equations. 5. Linearized theory. 6. Spherical bodies and Schwarzschild spacetime. 7. Bibliographical notes. 8. Exercises.

  6. Post-Minkowskian theory: formulation

    1. Landau-Lifshitz formulation of general relativity. 2. Relaxed Einstein equations. 3. Integration of the wave equation. 4. Bibliographical notes. 5. Exercises.

  7. Post-Minkowskian theory: implementation

    1. Assembling the tools. 2. First iteration. 3. Second iteration: near zone. 3. Second iteration: wave zone. 4. Bibliographical notes. 5. Exercises.

  8. Post-Newtonian theory: fundamentals

    1. Equations of post-Newtonian theory. 2. Classic approach to post-Newtonian theory. 3. Coordinate transformations. 4. Post-Newtonian hydrodynamics. 5. Bibliographical notes. 6. Exercises.

  9. Post-Newtonian theory: system of isolated bodies

    1. From fluid configurations to isolated bodies. 2. Inter-body metric. 3. Motion of isolated bodies. 4. Motion of compact bodies. 5. Motion of spinning bodies. 6. Point particles. 7. Bibliographical notes. 8. Exercises.

  10. Post-Newtonian celestial mechanics, astrometry and navigation

    1. Post-Newtonian two-body problem. 2. Motion of light in post-Newtonian theory. 3. Post-Newtonian gravity in timekeeping and navigation. 4. Spinning bodies. 5. Bibliographical notes. 6. Exercises.

  11. Gravitational waves

    1. Gravitational-wave field and polarizations. 2. The quadrupole formula. 3. Beyond the quadrupole formula: Waves at 1.5PN order. 4. Gravitational waves emitted by a two-body system. 5. Gravitational waves and laser interferometers. 6. Bibliographical notes. 7. Exercises.

  12. Radiative losses and radiation reaction

    1. Radiation reaction in electromagentism. 2. Radiative losses in gravitating systems. 3. Radiative losses in slowly-moving systems. 4. Astrophysical implications of radiative losses. 5. Radiation-reaction potentials. 6. Radiation reaction of fluid systems. 7. Radiation reaction of N-body systems. 8. Radiation reaction in alternative gauges. 9. Orbital evolution under radiation reaction. 10. Bibliographical notes. 11. Exercises.

  13. Alternative theories of gravity

    1. Metric theories and the strong equivalence principle. 2. Parametrized post-Newtonian framework. 3. Experimental tests of gravitational theories. 4. Gravitational radiation in alternative theories of gravity. 5. Scalar-tensor gravity. 6. Bibliographical notes. 7. Exercises.

Errors, typographical and otherwise

A number of errors were reported by readers. They have our gratitude.