# Gravitation (book)

Gravitation is a physics book on Einstein's theory of gravity, written by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler and originally published by W. H. Freeman and Company in 1973. It is frequently abbreviated MTW after its authors' last names. The cover illustration, drawn by Kenneth Gwin, is a line drawing of an apple with cuts in the skin to show geodesics. It contains 10 parts and 44 chapters, each beginning with a quotation. The bibliography has a long list of original sources and other notable books in the field. While this may not be considered the best introductory text because its coverage may overwhelm a newcomer, and despite the fact that parts of it are now out-of-date, it remains a highly-valued reference for advanced graduate students and researchers.[1]

Authors Charles W. MisnerKip S. ThorneJohn Archibald Wheeler Kenneth Gwin United States English General relativity Non-fiction W. H. Freeman Princeton University Press 1973, 2017 Print xxvi, 1279 .mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}0-7167-0344-0 585119 531/.14 QC178 .M57

## Content

### Subject matter

After a brief review of special relativity and flat spacetime, physics in curved spacetime is introduced and many aspects of general relativity are covered; particularly about the Einstein field equations and their implications, experimental confirmations, and alternatives to general relativity. Segments of history are included to summarize the ideas leading up to Einstein's theory. The book concludes by questioning the nature of spacetime and suggesting possible frontiers of research. Although the exposition on linearized gravity is detailed, one topic which is not covered is gravitoelectromagnetism. Some quantum mechanics is mentioned, but quantum field theory in curved spacetime and quantum gravity are not included.

The topics covered are broadly divided into two "tracks", the first contains the core topics while the second has more advanced content. The first track can be read independently of the second track. The main text is supplemented by boxes containing extra information, which can be omitted without loss of continuity. Margin notes are also inserted to annotate the main text.

The mathematics, primarily tensor calculus and differential forms in curved spacetime, is developed as required. An introductory chapter on spinors near the end is also given. There are numerous illustrations of advanced mathematical ideas such as alternating multilinear forms, parallel transport, and the orientation of the hypercube in spacetime. Mathematical exercises and physical problems are included for the reader to practice.

The prose in the book is conversational; the authors use plain language and analogies to everyday objects. For example, Lorentz transformed coordinates are described as a "squashed egg-crate" with an illustration. Tensors are described as "machines with slots" to insert vectors or one-forms, and containing "gears and wheels that guarantee the output" of other tensors.

### Sign and unit conventions

MTW uses the −+++ metric convention, and dissuades the use of the ++++ metric and imaginary time coordinate ict. In the front endpapers, the sign conventions for the Einstein field equations are established and the conventions used by many other authors are listed.

The book also uses geometrized units, the gravitational constant ${\displaystyle G}$  and speed of light in vacuum ${\displaystyle c}$  each set to 1. The back endpapers contain a table of unit conversions.

• List of Boxes
• List of Figures
• Forward to the 2017 Edition
• Preface to the 2017 Edition
• Preface
• Acknowledgements
• Part I: Spacetime Physics
• 1. Geometrodynamics in Brief
• Part II: Physics in Flat Spacetime
• 2. Foundations of Special Relativity
• 3. The Electromagnetic Field
• 4. Electromagnetism and Differential Forms
• 5. Stress-Energy Tensor and Conservation Laws
• 6. Accelerated Observers
• 7. Incompatibility of Gravity and Special Relativity
• Part III: The Mathematics of Curved Spacetime
• 8. Differential Geometry - An Overview
• 9. Differential Topology
• 10. Affine Geometry - Geodesics, Parallel Transport, and Covariant Derivatives
• 11. Geodesic Deviation and Spacetime Curvature
• 12. Newtonian Gravity in the Language of Curved Spacetime
• 13. Riemannian Geometry - Metric as Foundation of All
• 14. Calculation of Curvature
• 15. Bianchi Identities and the Boundary of a Boundary
• Part IV: Einstein's Geometric Theory of Gravity
• 16. Equivalence Principle and the Measurement of the "Gravitational Field"
• 17. How Mass-Energy Generates Curvature
• 18. Weak Gravitational Fields
• 19. Mass and Angular Momentum of a Gravitating System
• 20. Conservation Laws for 4-Momentum and Angular Momentum
• 21. Variational Principle and Initial-Value Data
• 22. Thermodynamics, Hydrodynamics, Electrodynamics, Geometric Optics and Kinetic Theory
• Part VI: The Universe
• Part VIII: Gravitational Waves
• 35. Propagation of Gravitational Waves
• 36. Generation of Gravitational Waves
• 37. Detection of Gravitational Waves
• Part IX: Experimental Tests of General Relativity
• Part X: Frontiers
• 41. Spinors
• 42. Regge Calculus
• 43. Superspace: Arenas for the Dynamics of Geometry
• 44. Beyond the End of Time
• Bibliography and Index of Names
• Subject Index

## Editions and translations

The book has been reprinted in English 24 times. Hardback and softcover editions have been published. The original citation is

It has also been translated into other languages, including Russian (in three volumes), Chinese,[2] and Japanese.[3]

This is a recent reprinting.

• Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald; Kaiser, David I. (2017). Gravitation. Princeton University Press. ISBN 9780691177793. Reprinting.

## Reviews

The book is still considered influential in the physics community, with generally positive reviews, but with some criticism of the book's length and presentation style. To quote Ed Ehrlich:[4]

"'Gravitation' is such a prominent book on relativity that the initials of its authors MTW can be used by other books on relativity without explanation."

James Hartle notes in his book:[5]

“Over thirty years since its publication, Gravitation is still the most comprehensive treatise on general relativity. An authoritative and complete discussion of almost any topic in the subject can be found within its 1300 pages. It also contains an extensive bibliography with references to original sources. Written by three twentieth-century masters of the subject, it set the style for many later texts on the subject, including this one.”

Sean M. Carroll states in his own introductory text:[6]

“The book that educated at least two generations of researchers in gravitational physics. Comprehensive and encyclopedic, the book is written in an often-idiosyncratic way that you will either like or not.”

Pankaj Sharan writes:[7]

“This large sized (20cm × 25cm), 1272 page book begins at the very beginning and has everything on gravity (up to 1973). There are hundreds of diagrams and special boxes for additional explanations, exercises, historical and bibliographical asides and bibliographical details.”

Ray D'Inverno suggests:[8]

“I would also recommend looking at the relevant sections of the text of Misner, Thorne, and Wheeler, known for short as ‘MTW’. MTW is a rich resource and is certainly worth consulting for a whole string of topics. However, its style is not perhaps for everyone (I find it somewhat verbose in places and would not recommend it for a first course in general relativity). MTW has a very extensive bibliography.”

Many texts on general relativity refer to it in their bibliographies or footnotes. In addition to the four given, other modern references include George Efstathiou et al.,[9] Bernard F. Schutz,[10] James Foster et al.,[11] Robert Wald,[12] and Stephen Hawking et al.[13]

Other prominent physics books also cite it. For example, Classical Mechanics (second edition) by Herbert Goldstein, who comments:[14]

“This massive treatise (1279 pages! (the pun is irresistible)) is to be praised for the great efforts made to help the reader through the maze. The pedagogic apparatus includes separately marked tracks, boxes of various kinds, marginal comments, and cleverly designed diagrams.”

The third edition of Goldstein's text still lists Gravitation as an "excellent" resource on field theory in its selected biography.[15]

## References

1. ^ Are There Any Good Books on Relativity Theory? MTW. John C. Baez et al. University of California, Riverside. September 1998. Accessed January 27, 2019.
2. ^ Kip Thorne. "Publications as of 7 June 2010". Retrieved 24 February 2016.
3. ^ "Juryoku riron : Gravitation koten rikigaku kara sotaisei riron made jiku no kikagaku kara uchu no kozo e. (Japanese)". amazon.com. Retrieved 24 February 2016.
4. ^ Ehrlich, Ed. "Gravitation - Book Review". sky-watch.com. Archived from the original on 2 February 2016. Retrieved 1 January 2015.
5. ^ J. B. Hartle (2003). Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley. p. 563. ISBN 9780805386622.
6. ^ S. Carroll (2003). Spacetime and Geometry: An Introduction to General Relativity. Addison-Wesley. p. 496. ISBN 9780805387322.
7. ^ P. Sharan (2009). Spacetime, Geometry and Gravitation. Springer. p. 34. ISBN 978-3764399702.
8. ^ R. D'Inverno (1992). Introducing Einstein's Relativity. Clarendon Press. p. 371. ISBN 9780198596868.
9. ^ M. P. Hobson; G. P. Efstathiou; A. N. Lasenby (2006). General Relativity: An Introduction for Physicists. Cambridge University Press. p. 555. ISBN 9780521829519.
10. ^ B. Schutz (1985). A First Course in General Relativity. Cambridge University Press. p. 362. ISBN 0521277035.
11. ^ Foster, J; Nightingale, J.D. (1995). A Short Course in General Relativity (2nd ed.). Springer. p. 222. ISBN 0-03-063366-4.
12. ^ R. M. Wald (1984). General Relativity. Chicago University Press. p. 479. ISBN 9780226870335.
13. ^ S. W. Hawking; W. Israel (1987). Three Hundred Years of Gravitation. Cambridge University Press. p. 327. ISBN 9780521379762.
14. ^ H. Goldstein (1980). Classical mechanics (2nd ed.). Addison-wesley. p. 333. ISBN 0-201-02918-9.
15. ^ Goldstein, Herbert, et al. Classical Mechanics. 3rd ed., Addison Wesley, 2002. ISBN 0201316110. p. 629.