Editing The Large Scale Structure of Space–Time

{{Short description|1973 book by S. W. Hawking and G. F. R. Ellis}}
{{Infobox book
| name              = The Large Scale Structure of Space–Time
| image             = The Large Scale Structure of Space-Time.jpg
| caption           = Cover of the first edition
| authors           = [[Stephen Hawking]]<br/>[[George F. R. Ellis|George Ellis]]
| country           = United Kingdom
| language          = English
| subject           = General relativity
| publisher         = [[Cambridge University Press]]
| pub_date          = 1973
| media_type        = Print ([[Hardcover]] and [[Paperback]])
| pages             = 384
| isbn              = 978-0521200165
| genre             = Non-fiction
}}

'''''The Large Scale Structure of Space–Time''''' is a 1973 [[treatise]] on the [[theoretical physics]] of [[spacetime]] by the physicist [[Stephen Hawking]] and the mathematician [[George F. R. Ellis|George Ellis]].<ref>{{cite book |last1=Gibbons |first1=G. W. |last2=Shellard |first2=E. P. S. |last3=Rankin |first3=S. J. |date=23 October 2003 |title=The Future of Theoretical Physics and Cosmology: Celebrating Stephen Hawking's Contributions to Physics |publisher=Cambridge University Press |isbn=978-0-521-82081-3 |page=177 |url=https://books.google.com/books?id=yLy4b61rfPwC&pg=PA177}}</ref> It is intended for specialists in general relativity rather than newcomers.<ref name=":22">{{Cite book |last1=McEvoy |first1=J. P. |title=Introducing Stephen Hawking |last2=Zarate |first2=Oscar |publisher=Totem Books |year=1995 |isbn=978-1-874-16625-2}}</ref>

==Background==
In the mid-1970s, advances in the technologies of astronomical observations – radio, infrared, and X-ray astronomy – opened up the Universe of exploration. New tools became necessary. In this book, Hawking and Ellis attempt to establish the [[axiom]]atic foundation for the geometry of four-dimensional spacetime as described by Albert Einstein's [[General relativity|general theory of relativity]] and to derive its physical consequences for [[Gravitational singularity|singularities]], horizons, and [[Causality (physics)|causality]]. Whereas the tools for studying Euclidean geometry were a straightedge and a compass, those needed to investigate curved spacetime are test particles and light rays.<ref name=":0" /> According to the mathematical physicist [[John C. Baez|John Baez]] from the [[University of California, Riverside]], ''The Large Scale Structure of Space–Time'' was "the first book to provide a detailed description of the revolutionary [[Differential topology|topological methods]] introduced by Penrose and Hawking in the early seventies."<ref>{{Cite web|url=http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html#advanced|title=Guide to Relativity Books|last1=Baez|first1=John|last2=Hillman|first2=Chris|date=October 1998|publisher=Department of Physics, University of California, Riverside.|access-date=August 25, 2019}}</ref>

Hawking co-wrote the book with Ellis, while he was [[postdoc|postdoctoral fellow]] at the [[University of Cambridge]]. In his 1988 book ''[[A Brief History of Time]]'', he describes ''The Large Scale Structure of Space–Time'' as "highly technical" and unreadable for the layperson.

The book, now considered a classic, has also appeared in paperback format and has been reprinted many times.{{ref|a|a}} A fiftieth anniversary edition was published by Cambridge University Press in February 2023.<ref>{{Cite book |last=Hawking |first=Stephen |url=https://www.worldcat.org/oclc/1347434162 |title=The large scale structure of space-time |date=2023 |others=George F. R. Ellis, Abhay Ashtekar |isbn=978-1-009-25316-1 |edition=50th anniversary |location=Cambridge, United Kingdom |oclc=1347434162}}</ref>

== Table of contents ==
* Preface
* 1. The Role of [[Gravity]]
* 2. [[Differential geometry|Differential Geometry]]
* 3. General Relativity
* 4. The Physical Significance of [[Curvature]]
* 5. [[Exact solutions in general relativity|Exact Solutions]]
* 6. [[Causal structure|Causal Structure]]
* 7. The [[Cauchy problem|Cauchy Problem]] in General Relativity
* 8. Space–time Singularities
* 9. [[Gravitational collapse|Gravitational Collapse]] and [[Black hole|Black Holes]]
* 10. The Initial Singularity of the Universe
* Appendix A: Translation of An Essay by [[Pierre-Simon Laplace|P. S. Laplace]]
* Appendix B: Spherically Symmetric Solutions of [[Birkhoff's theorem (relativity)|Birkhoff's Theorem]].
*References
*Notation
*Index

== Assessment ==
Mathematician [[N. M. J. Woodhouse|Nicholas Michael John Woodhouse]] at the University of Oxford considered this book to be an authoritative treatise that could become a classic. He observed that the authors begin with axioms of geometry and physics then derive the consequences in a rigorous fashion. Various well-known exact solutions to Einstein's field equations and their physical meaning are explored. In particular, Hawking and Ellis show that singularities and black holes arise in a large class of plausible solutions. He warned that although this book is self-contained, it is more suitable for specialists rather than new students as it is heavy-going and contains no exercises. He noted that despite the authors' attempt at a rigorous treatment, certain technical terms, such as Lie groups, are used but never explained, and that modern coordinate-free methods are introduced, but not used effectively.<ref>{{Cite journal|last=Woodhouse|first=Nicholas|date=1974|title=The Large Scale Structure of Space–Time|journal=Physical Bulletin|volume=25|issue=6|pages=238|doi=10.1088/0031-9112/25/6/029}}</ref>

Theoretical physicist [[Rainer K. Sachs|Rainer Sachs]] from the University of California, Berkeley, observed that ''The Large-Scale Structure of Space–Time'' was published within just a few years as ''Gravitation and Cosmology'' by Steven Weinberg and ''[[Gravitation (book)|Gravitation]]'' by Charles Misner, Kip Thorne, and John Archibald Wheeler. He believed these three books can supplement each other and lead students to the forefront of research. Whereas Hawking and Ellis employ global analysis extensively but say relatively little about [[Perturbation theory|perturbative methods]], the other two books neglect global analysis and cover in great detail perturbations. He believed Hawking and Ellis did a great job summarizing recent developments in the field (as of 1974) and that the intended audience is a doctoral student (or higher) with a strong mathematical background and prior exposure to general relativity. He argued that the core of the books consists of two chapters, Chapter 4 on the significance of spacetime curvature and Chapter 6 on causal structure, and that the most interesting application is the penultimate chapter on black holes. He noted that mathematical arguments are at times difficult to follow and suggested ''Techniques of Differential Topology in Relativity'' by [[Roger Penrose]] for reference. He also noticed a small number of errors, though none affect the general conclusions drawn by the authors. He thought that this book is a "model" presentation on the interplay between mathematics and physics that could become highly influential in the future.<ref>{{Cite journal|last=Sachs|first=Rainer|date=April 1974|title=The Large Scale Structure of Space–Time|journal=Physics Today|publisher=American Institute of Physics|volume=27|issue=4|pages=91–3|doi=10.1063/1.3128542|bibcode=1974PhT....27d..91H|s2cid=121949888}}</ref>

Theoretical physicist [[John Archibald Wheeler]] of Princeton University recommended this book to anyone interested in the implications of general relativity for cosmology, the singularity theorems, and the physics of black holes, presented in an almost Euclidean fashion, though he acknowledged that this is not a textbook due to its lack of examples and exercises. He praised its 62 illustrative diagrams.<ref name=":0">{{Cite journal|last=Wheeler|first=John A.|date=March–April 1975|title=The Large Scale Structure of Space–Time by S. W. Hawking and G. F. R.Ellis|department=Review|journal=American Scientist|publisher=Sigma Xi, The Scientific Research Honor Society|volume=62|issue=2|pages=218|jstor=27845370}}</ref>

== See also ==
{{Portal|Books|Physics}}
* [[General relativity#Further reading|List of books on general relativity]]

==Notes==
<ol type="a">
<li>{{note|a}} {{cite book |last1=Hawking |first1=S. W. |author-link1=Stephen Hawking |last2=Ellis |first2=G. F. R. |author-link2=George Francis Rayner Ellis |date=1973 |title=The Large Scale Structure of Space–Time |publisher=Cambridge University Press |isbn=0-521-09906-4}}
</ol>

==References==
{{Reflist}}

{{Stephen Hawking}}

{{DEFAULTSORT:Large Scale Structure Of Spacetime, The}}
[[Category:1973 non-fiction books]]
[[Category:Books by George F. R. Ellis]]
[[Category:Books by Stephen Hawking]]
[[Category:Cambridge University Press books]]
[[Category:Collaborative non-fiction books]]
[[Category:English-language non-fiction books]]
[[Category:Physics education in the United Kingdom]]
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