Book Description
Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general relativity. With an accessible and lively writing style, it introduces modern techniques to what can often be a formal and intimidating subject. Readers are led from the physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology. For advanced undergraduates and graduate students, or anyone interested in astronomy, cosmology, physics, or general relativity.
Customer Reviews:
Wordy and Wonderful.......2006-12-12
This is an advanced text, but all the same it is not particularly rigorous or dense, so it is in principle accessible to the beginner. With an easy authority, Carroll leads us on a wandering journey through the mystical lands of general relativity. This is very different from, and compliments nicely, the clarity and directness of Wald. As a student of GR, I use Wald for the bottom line on any subject, and Carroll for the random physical or computational insights that I invariably find in any section of the book. Carroll's prose is like music to the ear and I always enjoy myself when I decide to open up this book.
Be warned that there are lots of mistakes in this first edition--you might want to wait for the second one.
Also, his chapter on cosmology is better than any I've seen.
BY FAR the best book on GR.......2006-10-21
I am currently on the 4th chapter of Carroll's "Spacetime and Geometry" and thus far I am amazed at how clear it is. Sure there is a lot of math in it however that also is very clearly explained. In fact, I think that Carroll explains the differential geometry material better than any mathematician has in any book on the subject. If you want to learn general relativity, there is no getting around the math; sooner or later you'll have to learn it. I'd suggest, especially if you are self-studying the subject, to rather pick up this book and go through it than pick up a more "elementary" text and a book on Riemannian geometry to look at later.
(Although I do also highly recommend Kay's (Schaum outline) "Tensor Calculus" for self study. The prima donnas don't like Kay's book because it "doesn't have enough theory." I suppose if a freshman calculus book does not have the Lebesgue integral defined in ti they'll complain about that too.)
Because, you can always skip through certain sections if the math is too heavy and go back through it later. And like I wrote earlier, you won't find a better introduction to the mathematical material than here.
Carroll should be given the Nobel prize for this book. If not in Physics, then in literature. I'd give this textbook 10 stars if I could.
A nice blend of the ideas of physics with mathematics.......2006-04-11
Kudos to Carroll.
This book is an excellent INTRODUCTION to SR and GR for the graduate physics student as well as the graduate mathematics students.
Pure mathematics often loses sight of the ideas which motivated it and physics often loses the mathematical foundations from which it is built.
This book offers some level of mathematical formalism to the physics student while exposing the ideas motivating the mathematical concepts.
I particularly like how he builds up the mathematical machinery of GR by introducing sets then topology on this set giving a topological space. Now he adds in the ideas of a manifold which make this topological space look like Rn locally with the patches sewn together smoothly. The manifold comes equipped with tangent space, cotangent spaces and their product spaces giving tensor spaces. These are defined nicely with reference to component formalism as well as the multilinear algebra approach as maps from products spaces to the reals, etc. He delves into forms and tantalized the reader with deRham cohomology although doesnt go into it. He shows how these can be differentiated ( exterior derivative ) and integrated.
Now the metric is introduced giving a geometry. To this is added a connection which is independent of the metric and leads to notions of parallel transport and differentiation of tensors ( covariant derivative ). One sees that in a special case one can derive a unique connection from the metric ( Levi-Cevita ) which is used in GR.
Fibre bundles, Lie derivatives, pullbacks etc are introduced as needed.
He then presents some introductory GR material by applying the mathematics.
Great Book But Won't Get You To The Promised Land.......2005-12-14
My comments come with a few caveats.
1. This is my fourth GR book.
2. I'm not hardcore into physics. I'm not a physic grad and I'm reading GR for fun. I have a decent graduate math background but I've been corrupted with 10+ years in working in various roles software engineering, electronics engineering and marketing.
3. I assume that since you're considering buying this book, you're goal is to get at the "real" GR, not the watered down discover channel version.
With these caveats in mind, here are my comments.
First, on a scale of 1-5, I rank Carroll at level 3 in terms of math/physics maturity and thoroughness. Here is my full ranking of authors from my limited reading: 1. schutz 2. hartle 3. penrose 3. carroll 4. wald 5. physics journal articles
Second, using the rankings above, I recommend Carroll as the second port of entry. If you're comfortable with multivariable calculus, start with schutz (#1). You'll get warm fuzzies doing the toy exercises. But Schutz is tensor/math-lite. If you've had advanced calculus and geometry already, jump in with carroll (#3). But you'll be hard-pressed to find anyone else as polite to the reader. He won't prepare you for 80 percent of what's published. If you're ready to throw off the training wheels and jump dive into mainstream GR go with Wald (#4).
Note that Hartle (#2) is a good "tweener" book with feel-good exercises and some of the full-on GR equations at the end. I bet most instructors teaching a first year grad course would go with Hartle along with a dose of supplementary material.
Third, don't expect Carroll to be your last GR book purchase if you want to reach the promised land (see caveat #4). Living and breathing GR is found in physics journals and for that you'll need Wald or another advanced GR book.
good math chapters, not at beginner's level after that.......2005-03-07
I had a course based on that book and I've read chapters 1-6 (out of 9 chapters total) plus all the appendices. Also, I've solved some of the problems.
Please keep in mind my review is from a beginner point of veiw. Readers more experienced in GR may feel different but that book is supposedly written for beginners right?
The math chapters 2 and 3 are worth reading because they will teach you tensor analysis on manifolds in much clearer way than other books. The book makes a clear distinction between assumptions, choices (like working with a metric compatible connection), or derived facts. It is nice that the book makes a difference between a Christoffel connection and a generic connection. The appendices are worth reading too cause they will give you a feeling for some new to you math necessary for GR like pullbacks, Lie Derivatives, hypersurfaces etc.
Chapter 4 is worth reading too cause it makes clear that Einstein's equations are just the simplest guess out of many other possibilities. Also it shows how we generalize physical laws from special relativity to GR making it clear our choices are the simplest ones but not the only ones possible.
The chapters after that discuss applications of GR like black holes, gravitational radiation, cosmology etc. Of these, I've read only the black holes chapters 5 and 6 and I wasn't able to understand 100% what was goin on. The problem was that the book uses concepts that you still don't quite understand if you are a beginner like 'spacelike singularity' or 'conformal diagrams'. That is informative but the book doesn't provide the necessary level of detail and examples for beginners so you could really master such concepts and use them in your practise.
There are problems after each chapter but not the necessary beginners problems that increase your conceptual understanding of the theory. Instead, some of the problems are just tedious algebra of type 'find the curvature for some general form of the metric' for which specialists in the field use symbolic programs like Mathematica. Solving these by hand proves that you can take derivatives and you are a mazochist but not that you understand GR. Other problems are really relevant to your education but are not dirrectly connected to the discussion in the text. Because of that you have to solve them from scratch and it will take you ages ...
If you are a beginner like me, you should read the math chapters and all appendices of Carroll's book plus chapter 4. Then you should read a real book for beginners with a lot of examples how to apply GR in real calculations and how to understand it. For that I recommend James Hartle's "Gravity: An Introduction to Einstein's General Relativity" and Bernard Schutz's "A first course in General Relativity". After that hopefully you will understand the rest of Carroll's book better. My experience was that often I had to read Hartle's book in order to understand and solve a problem in Carroll's book.
Book Description
Exposition of 4th dimension, concepts of relativity as Flatland characters continue adventures. Popular, easily followed yet accurate, profound. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Accessible to lay readers but also of interest to specialists. Includes 141 illustrations.
Customer Reviews:
With few exceptions, it is a readable, stepwise explanation of how the universe is structured.......2007-06-29
To understand relativity, it is necessary to understand geometry, specifically how a straight line can be curved. For nearly everyone, any attempt to understand four-dimensional space begins with understanding how a three-dimensional creature would appear to a two-dimensional one. One of the earliest and still the greatest of all introductions to going up a dimension is "Flatland" by Edwin A. Abbott. Quite naturally and sensibly, Rucker starts with Abbott's rendition of the properties of Flatland.
Rucker then moves on to the idea of curved space, where the shortest distance between two points is a "straight line", which is curved by the properties of the space. The space that we occupy is curved by the presence of matter, as Einstein claimed in his relativity theories. Furthermore, movement causes shrinkage in the direction of the movement and the slowing of time, which causes time to become just another dimension of space. As counterintuitive as this may appear, Einstein's relativity theory has been verified over and over again to a large number of significant figures.
One of the best things about this book is that Rucker has included problems at the end of each chapter. These problems reinforce the concepts of the chapter; it is unfortunate that no solutions were included.
In this book, Rucker steps the reader through all of the background material necessary to understand relativity and four-dimensional space. With few exceptions, the accounts are understandable to anyone with an understanding of college algebra.
The best book ever in its field.......2007-04-19
This book has presented the most difficult topics of our world with the easiest words. After reading this book many of my questions that I had in my mind for a long time were answered. It's worth thousands more than its price.
Congratulation to Mr. Rudolf Rucker for his great book.
explain dimensions very well.......2007-03-31
it is published years before but it is almost new for today and it explain dimensions and shape of space well and clearly .thanx to amazon for sending me timely.
See what's outside the box.......2007-03-30
Over two millenia ago, Euclid wrote his masterpiece Elements and stated in his fifth postulate that only one perpendicular line could pass through any one point adjacent to another line.
One hundred fifty years ago, it was proven that yet another geometry could be described by asserting that more than one parallel line could pass through such a point.
Building on these ideas, Rucker briefly yet thoroughly surveys the relevant mathematics outside the box of Euclidian geometry.
It's a fascinating place too because it involves considerations of hyperspace, four dimensional travels and ultimately Einstein's theory of relativity.
Copiously filled with illustrations to help drive home his points, Rucker has produced a book that meaningful helps one visualize and better understand the fourth dimension.
This book is an excellent read along with Choas, Coincidences and All that Math Jazz, The Fourth Dimension Simply Explained, Einstein's own Relativity and Hyperspace by Michio Kaku which discusses all these ideas as well as contemporary string theory (which purports to pull it all together).
excellent book, fascinating author, start your exploration! :).......2005-12-31
Mr. Rucker is a 'genius educator' in my opinion :) he can open your mind and get you started - no matter what direction you wanna take! :) whether it be philosophy, math, physics, or even spirtual things - Mr. Rucker can get you going! to me, he is one of the great men of these modern times :) ah, i remember! pay particular attention to visualizing hyper-dimensional objects .. it can be done! good luck and may god bless all of you! :)
Customer Reviews:
paperback version.......2006-02-04
If you're looking for the paperback version, look for ISBN 0395393884. It doesn't show up as the paperback version of this hardback, probably because the author's name for the paperback is listed as Rudolph Rucker instead of Rudy Rucker.
Hope this helps.
Good overview.......2003-06-16
This book presents its material in a well-organized manner.
The author is a brilliant theoretical physicist and explains the concepts wonderfully.
I recommend this book for any and all who wish to understand the essence of time, reality, and the universe in general.
From a very personal level, the book affirms many of my own views pertaining to the cosmos and consciousness. There is indeed a Primary Mover (aka "God"), and he exists and operates in infinite (!) dimensions.
Nice intro to 4-D.......2003-05-04
I bought this book about ten years ago, and recently rediscovered it. It is full of nice (though very simplistic) illustrations and lots of references to other books and writers that touch the subject. Not very profound, but enough to tickle the mind and awaken interest for futher investigation into this realm. Rucker has obviously read a lot on this matter and he has made me want the same.
Would you please repeat that........2002-11-04
I found this book a difficult read. "Flatland" by A. Square (an illustrator) is a definite pre-requisite, and helpful, but even with that under my belt I had problems following Mr. Rucker.
Book Description
This book, based on a graduate course on Riemannian geometry and analysis on manifolds, held in Paris, covers the topics of differential manifolds, Riemannian metrics, connections, geodesics and curvature, with special emphasis on the intrinsic features of the subject. Classical results on the relations between curvature and topology are treated in detail. The book is quite self-contained, assuming of the reader only differential calculus in Euclidean space. It contains numerous exercises with full solutions and a series of detailed examples which are picked up repeatedly to illustrate each new definition or property introduced.
For this third edition, some topics about the geodesic flow and Lorentzian geometry have been added and worked out in the same spirit.
Book Description
Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity. Although the original audience was made up of mathematics students, the focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle. At centre stage are the "local inertial coordinates" set up by an observer in free fall, in which special relativity is valid over short times and distances.
In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors. The basic theory is presented using techniques, such as phase-plane analysis, that will already be familiar to mathematics undergraduates, and numerous problems, of varying levels of difficulty, are provided to test understanding. The latter chapters include the theoretical background to contemporary observational tests - in particular the detection of gravitational waves and the verification of the Lens-Thirring precession - and some introductory cosmology, to tempt the reader to further study.
While primarily designed as an introduction for final-year undergraduates and first-year postgraduates in mathematics, the book is also accessible to physicists who would like to see a more mathematical approach to the ideas.
Book Description
This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.
Customer Reviews:
Complete introduction to spinors and space-time physics.......2006-04-16
This book provides a very comprehensive account of two-spinor calculus, along with some of its applications to physics. This material is intrinsically interesting and has some applications to physics, in addition it also provides the background needed to study volume II. The second volume covers applications to physics in more detail and twistors too.
Spinors unquestionably play a central role in quantum mechanics. Some problems in general relativity are certainly more transparent when approached with spinors, as compared to the usual tensor analysis. This combined with the fact that one can roughly view a spinor as the square root of a null vector and considering things like Dirac's scissors suggest the possibility that spinors are more fundamental than tensors and may provide a deeper insight into the nature of space-time than tensors do. This is one of the main themes of the book, I personally find the arguments intriguing.
The first two chapters establish the geometry and algebra of spinors. The pace is reasonable and the approach is very geometrical. Then the correspondence between tensors and spinors is developed. First the authors show how to represent tensors as spinors and then they show how to represent spinors as tensors. As an application of this they show how a Lorentz transformation is represented by two spin transformations. This is followed by a chapter that takes many concepts from differential geometry and puts them in spinor form, including Einstein's equation.
The final chapter mostly considers fields formulated in terms of spinors. This includes the electromagnetic field, Yang-Mills fields (a nice introduction to fibre bundles is included) and general relativity.
On the whole I think this book provides an excellent development of two-spinor calculus, with a nice emphasis on the geometry of spinors. It takes some familiar fields, such as the electromagnetic field, and formulates them in terms of spinors. However, one thing I thought was missing was more extended discussions of the known situations in general relativity where spinor methods prove more useful than tensor methods, e.g. the classification of the Weyl tensor or Witten's proof of the positive energy theorem. More material like this is presented in volume II. This book also gives some general arguments that spinors may be more fundamental than tensors and hence provide more insight into the nature of space-time, in fact this is one of the central themes of the book. I find the arguments to be very plausible, but I think it's safe to say that even twenty years after the publication of the book that it has yet to be demonstrated.
Book Description
In this insightful book, which is a revisionist math history as well as a revisionist art history, Tony Robbin, well known for his innovative computer visualizations of hyperspace, investigates different models of the fourth dimension and how these are applied in art and physics. Robbin explores the distinction between the slicing, or Flatland, model and the projection, or shadow, model. He compares the history of these two models and their uses and misuses in popular discussions. Robbin breaks new ground with his original argument that Picasso used the projection model to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The discussion is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, quasicrystals, and quantum topology. Robbin clarifies these esoteric concepts with understandable drawings and diagrams.
Robbin proposes that the powerful role of projective geometry in the development of current mathematical ideas has been long overlooked and that our attachment to the slicing model is essentially a conceptual block that hinders progress in understanding contemporary models of spacetime. He offers a fascinating review of how projective ideas are the source of some of today’s most exciting developments in art, math, physics, and computer visualization.
Customer Reviews:
A wonderful introduction to the projective approach in math and art.......2006-03-07
An innovative thinker and a gifted artist, Tony Robbin filters the world of mathematics through the nuances of human vision, creating masterful representations of higher dimensions. His new book stands as a testament to his meticulous scholarship of the history of projective geometry, in mathematics, physics and art. It is a thoroughly enjoyable account of how the notion of finding shadows of the fourth dimension emerged in the 19th century, permeated modern art in the 20th, and now represents one of the frontiers of computer graphics in the 21st. Along the way, Robbin shows how projective geometry could provide the key to a quantum description of gravity. A must read, for the curious anecdotes, cutting-edge science, impressive array of references, colorful art, and insight into how we can perceive the seemingly imperceptible.
Average customer rating:
- Essential for an advanced student of relativity
|
Global Lorentzian Geometry (Pure and Applied Mathematics)
John K. Beem ,
Paul Ehrlich , and
Kevin Easley
Manufacturer: CRC
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ASIN: 0824793242 |
Book Description
Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.
Customer Reviews:
Essential for an advanced student of relativity.......2005-11-16
My review is based on a previous edition of this text. I have seen the new (2nd) edition and it appears that several chapters have been added but the old chapters are essentially the same.
As of the time of this writing, I have only made it to the 2nd chapter (again, of the 1st edition). Nevertheless, I've read the introductory material in the introductory (1st) chapter several times, because it is so rich.
This text is perhaps most useful to a student who knows a few things about differential, to be more precise, Riemannian geometry (and is interested in general relativity). There are many differences between a Riemannian manifold and a Lorentzian manifold, where the latter metric is not positive definite in that the metric gives one negative eigenvalue. This text is quick to point out the differences, which is a great aid in understanding the new material.
I have some background in general relativity and from my experience in the subject there were many questions I had unanswered. This book is a blessing to me in that it has uncovered for me some of the mystery of Lorentzian manifolds, in particular space-times. There are still many things I do not understand but I am confident this text will aid me in getting a clearer picture.
I highly recommend this text to student of relativity theory who has an understanding of mathematical reasoning, and yearns for a stronger mathematical understanding of the Lorentzian manifold. The current edition is a bit expensive but even if you do not think it is worth it there are still some 1st editions floating around (#67 in the Dekker Pure & Applied Math Series) which are much cheaper. I may eventually buy the 2nd edition if I find the additional chapters make the book worth the price.
Book Description
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.
Customer Reviews:
A Stimulating and Interesting Book.......2000-11-01
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.
Average customer rating:
- makes a good mousepad
- A fantastic book for those who can understand it.
|
The Geometric Universe: Science, Geometry, and the Work of Roger Penrose
Manufacturer: Oxford University Press, USA
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The Large, the Small and the Human Mind
ASIN: 0198500599 |
Book Description
This collection has been inspired by the work of Roger Penrose. It gives an overview of current work on the interaction between geometry and physics, from which many important developments in research have emerged. This volume collects together the contributions of many important researchers, including Sir Roger himself, and gives an overview of the many applications of geometrical ideas and techniques across mathematics and the physical sciences. From the area of pure mathematics papers are included on the topics of classical differential geometry and non-commutative geometry, knot invariants, and the applications of gauge theory. Contributions from applied mathematics cover the topics of integrable systems and general relativity. Current research in experimental and theoretical physics inspired chapters on string theory, quantum gravity, the foundations of quantum mechanics, quasi-crystals and astrophysics. The collection also includes articles on quantum computation, quantum cryptography and the possible role of micro-tubules in a theory of consciousness.
Customer Reviews:
makes a good mousepad.......2002-02-08
This book makes the greatest mousepad I've ever had. Good book.
A fantastic book for those who can understand it........2000-05-27
A great book, about some of the coolest and most cutting edge theories out there. Certainly not for the layman though. Most of the chapters are filled with equation after equation however those with advanced math and a good math program will have lots of fun. This book is the real deal! Read it all and you just might fry your brain! It would get five stars if it was better organized. The best use of this book is for quick reference if you have a specific idea or question about the topics contained and don't or can't get to the internet. Not a must buy but worth the money.
Books:
- Spacetime and Geometry: An Introduction to General Relativity
- Spacetime and Geometry: An Introduction to General Relativity
- Spectral Methods: Fundamentals in Single Domains (Scientific Computation)
- Stability and Transition: Theory and Application: Efficient Numerical Methods with Computer Programs
- Table of Isotopes, 8th Edition
- The Black Swan: The Impact of the Highly Improbable
- The Classical Theory of Fields, Fourth Edition: Volume 2 (Course of Theoretical Physics Series)
- The Craft of Scientific Presentations: Critical Steps to Succeed and Critical Errors to Avoid
- The Data Warehouse Toolkit: The Complete Guide to Dimensional Modeling (Second Edition)
- The Geometry of Physics: An Introduction, Second Edition
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