Newtonian, post-Newtonian, Relativistic
Eric Poisson and Clifford M. Will
Honorable mention, Textbook/Physical Sciences and Mathematics,
(The American Publishers Awards for Professional and
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
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.
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.
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.
1. Spacetime. 2. Relativistic
hydrodynamics. 3. Electrodynamics. 4. Point particles in
spacetime. 5. Bibliographical notes. 6. Exercises.
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.
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.
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.
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.
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.
Post-Newtonian celestial mechanics, astrometry and
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.
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.
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.
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.