Naber provides an elementary introduction to the geometrical methods and notions used in special and general relativity. Particular emphasis is placed on the ideas concerned with the structure of space-time and that play a role in the Penrose-Hawking singularity theorems. The author's primary purpose is to give a rigorous proof of the simplest of these theorems, by the one that is representative of the whole. He provides exercises and examples at the end of each chapter. No previous exposure either to relativity theory of differential geometry is required of the reader, as necessary concepts are developed when needed, though some restrictions ae imposed on the types of space considered.
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"...fills a need to introduce the singularity theorems, their concepts and techniques to seniors or beginning graduate students." Physics in Canada
Book Description
An elementary introduction to the geometrical methods and notions used in special and general relativity. Emphasizes the ideas concerned with structure of space-time that play a role in Penrose-Hawking singularity theorems.
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13 of 13 people found the following review helpful:
4.0 out of 5 stars
A Stimulating and Interesting Book,
By Andy Gregory (Cleveland England) - See all my reviews
This review is from: Spacetime and Singularities: An Introduction (London Mathematical Society Student Texts) (Paperback)
This book is concerned primarily with a geometrical and in places, a topological approach to spacetime, leading to a full proof of one of Hawking's singularity theorems.The first part introduces the geometry of Minkowski Spacetime as.. 'a 4-dimensional ral vector space on which is defined a nondegenerate symmetric bilinear form of index one'.Some mathematical maturity is required to attempt this book on one's own.Chapter two develops relativistic mechanics in quite an abstract way (certainly for a first encounter) and chapter three develops spacetimes from the point of view of maps between manifolds.This chapter ends with a statement of one of Hawking's theorems. Chapter four sets out a full rigorous proof. There are no hints/partial solutions for the exercises although there are some 'examples'. The first three chapters were enjoyable and I managed to do quite a lot of the exercises and problems.As someone who works entirely independently at this kind of thing for 'fun',I found chapter four very hard going.Having no-one to ask when stuck made it a bit frustrating.The book was very stimulating though and encouraged me to research other sources for similar material to fill in gaps in my mathematical knowledge.
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Minkowski spacetime is a 4-dimensional real vector space M on which is defined a nondegenerate symmetric bilinear form g of index one; elements of M will be called events. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
admissible coordinatization, spinor map, causal trip, admissible frame, admissible observer, smooth timelike curve, proper time length, global time function, free material particle, chronology condition, stable causality, admissible basis, time orientable, variation vector field, spacelike slice, timelike curves, causal curve, coordinate patch, same time orientation, timelike geodesic, longitudinal curves, null cone, globally hyperbolic, unit normal field, timelike vectors Key Phrases - Capitalized Phrases (CAPs): (learn more)
Reversed Triangle Inequality, Inverse Function Theorem New!
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Minkowski spacetime is a 4-dimensional real vector space M on which is defined a nondegenerate symmetric bilinear form g of index one; elements of M will be called events. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
admissible coordinatization, spinor map, causal trip, admissible frame, admissible observer, smooth timelike curve, proper time length, global time function, free material particle, chronology condition, stable causality, admissible basis, time orientable, variation vector field, spacelike slice, timelike curves, causal curve, coordinate patch, same time orientation, timelike geodesic, longitudinal curves, null cone, globally hyperbolic, unit normal field, timelike vectors Key Phrases - Capitalized Phrases (CAPs): (learn more)
Reversed Triangle Inequality, Inverse Function Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 10
books:
See all 10 books this book cites
5
books
cite this book:
- The Principle of Relativity (Dover Books on Physics) by Albert Einstein in Back Matter
- Topological Methods in Euclidean Spaces (Dover Books on Mathematics) by Gregory L. Naber in Back Matter
- General Relativity for Mathematicians in Back Matter
- Relativity: The Special Theory by John Lighton Synge in Back Matter
- Spacetime Physics by Edwin F. Taylor in Back Matter
See all 10 books this book cites
- Analytic Philosophy Without Naturalism (Routledge Studies in Twentieth Century Philosophy) by Antonella Corradini in Back Matter
- Foundations and Applications of Multi-Agent Systems: UKMAS Workshop 1996-2000, Selected Papers (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence) by Mark d'Inverno on page 150
- Artificial Intelligence and Cognitive Science: 13th Irish International Conference, AICS 2002, Limerick, Ireland, September 12-13, 2002. Proceedings ... / Lecture Notes in Artificial Intelligence) by Michael O'Neill on page 44
- Philosophy of Religion: A Reader and Guide by William Lane Craig on page 112
- Naturalism: A Critical Analysis (Routledge Studies in Twentieth Century Philosophy) by William Craig on page 245
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