Global Lorentzian Geometry (Pure and Applied Mathematics)

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.

Introduction to General Relativistic and Scalar-Tensor Cosmologies

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Introduction to General Relativistic and Scalar-Tensor Cosmologies
Marcelo Samuel Berman
Manufacturer: Nova Science Publishers
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Binding: Hardcover

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ASIN: 1600210139

The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity

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Special Relativity for the graduate student.
Fascinating but not for the general reader

The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity
Gregory L. Naber
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486432351

Book Description

This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; the theory of spinors; and more. 1992 edition. 43 figures.

Customer Reviews:

Special Relativity for the graduate student........2007-01-18

This book is NOT for the pop science buff or the novice with little understanding of Special Relativity.

This book is designed for graduate level students in mathematics or physics who want a deeper understanding of Minkowski space. It presupposes a solid foundation in SR.

Having said this, the book is phenomenal. It brings out startling relationship between mathematics and physics explaining esoteric phenomena in SR.

For example:

1) The author shows how Lorentz transformations can be realized as fractional linear transformations of the Riemann sphere. By doing so we can use the full power of complex analysis to derive far reaching results. One property of such tranforms is that they map circles to circles thus explaining why an observer at rest who sees a circle ( say lit by lights ) will also see a circle, NOT ellipse from length contraction, when he moves relative to the circle.

2) Using a simple example ( scissors, chair and rubber band ) the author shows how a 360 degree rotation may not leave a system in the same state requiring the need of a new mathematical object ( spinor ) to describe this transformation.

3) The author clearly develops the mathematics of spinors. In fact this is the best introduction to spinors I have read. He develops the notion of spin vectors and realizes spinors as multi-linear functionals with inputs as spin vectors, their duals, their conjugate, and the conjugate duals. He then lays out the transformation properties of the spinors and shows that certain spinors have exactly the transformation properties needed to model particles with spin.

4) There is a great section on the relationship of SL (2,C) to the lorentz group. The author shows how Minkowski space can be represented by certain combinations of 2x2 complex matrices and shows how SL ( 2,C) can then operate on these. This operation is actually equivalent to a lorentz transformation thus giving a mapping between the two groups. He then shows that we can easily analyze SL (2,C) by breaking it down into irreducible representations ( which are known ) and that to each of these representations there exist a unique representation of the Lorentz group ( provided certain conditions are imposed ). If that condition is not met the representation leads to the all familiar 2-valued representation of the Lorentz group one hears so much about. Thus by studying SL ( 2,C ) which we know alot about we can represent the Lorentz group which is generally harder to study but of the most relevance in physics.

The books is filled with such insights and I would recommend it to anyone who wishes to understand particle physics or relativity.

Fascinating but not for the general reader.......2006-06-29

Starting with a quick overview of certain structures from linear algebra (bilinear forms) the book moves to discussing Minkowski spacetime. Unfortunately for many, the text is highly esoteric without even a single descriptive section that doesn't make use of some fairly advanced mathematics.

The level of mathematical maturity required is comparable to a fourth year mathematics major at any decent university. The relationship between the mathematics involved and the special theory of relativity is fully explained.

A solid introduction to special relativity for the earnest mathematician.

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Free SF Reader
Wonderful experience
A Valuable Idea for Science and Math Teachers
My favorite book to teach
A Good Book for Looking at the World Differently

Flatland
Edwin Abbott Abbott
Manufacturer: Princeton University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0691025258

Amazon.com

Unless you're a mathematician, the chances of you reading any novels about geometry are probably slender. But if you read only two in your life, these are the ones. Taken together, they form a couple of accessible and charming explanations of geometry and physics for the curious non-mathematician. Flatland, which is also available under separate cover, was published in 1880 and imagines a two-dimensional world inhabited by sentient geometric shapes who think their planar world is all there is. But one Flatlander, a Square, discovers the existence of a third dimension and the limits of his world's assumptions about reality and comes to understand the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England. The further mathematical fantasy, Sphereland, published 60 years later, revisits the world of Flatland in time to explore the mind-bending theories created by Albert Einstein, whose work so completely altered the scientific understanding of space, time, and matter. Among Einstein's many challenges to common sense were the ideas of curved space, an expanding universe and the fact that light does not travel in a straight line. Without use of the mathematical formulae that bar most non-scientists from an understanding of Einstein's theories, Sphereland gives lay readers ways to start comprehending these confusing but fundamental questions of our reality.

Book Description

Over a hundred years ago, Edwin Abbott Abbott wrote a mathematical adventure set in a two-dimensional plane world, populated by a hierarchical society of regular geometrical figures-who think and speak and have all too human emotions. Since then Flatland has fascinated generations of readers, becoming a perennial science-fiction favorite. By imagining the contact of beings from different dimensions, the author fully exploited the power of the analogy between the limitations of humans and those of his two-dimensional characters.

A first-rate fictional guide to the concept of multiple dimensions of space, the book will also appeal to those who are interested in computer graphics. This field, which literally makes higher dimensions seeable, has aroused a new interest in visualization. We can now manipulate objects in four dimensions and observe their three-dimensional slices tumbling on the computer screen. But how do we interpret these images? In his introduction, Thomas Banchoff points out that there is no better way to begin exploring the problem of understanding higher-dimensional slicing phenomena than reading this classic novel of the Victorian era.

Download Description

Flatland is about a two-dimensional world in which geometric shpates are the main charaters. The Square is the narrator of the book and he tells of his world and his fantastic contact with the three dimensional world. Mildly amusing and though provoking, a wonderful read for everyone! This book is easy to read in true text, not scanned images that can sometimes be difficult to decipher. This eBook has bookmarks at chapter headings and is printable.

Customer Reviews:

Free SF Reader.......2007-09-03

Flat is an exercise in science fiction geometry, if you like. It shows a denizen of a 2 dimensional world seeing what it would be like to exist in higher dimensions. An interesting mathematical and philosophical exercise. Some will definitely find this very odd, and rather quirky. If you don't know what a dimension means in this sense, give it a miss.

Wonderful experience.......2007-08-09

Smooth transaction, careful and fast shipping, very nice product, couldn't ask for a more wonderful buying experience. Thank you very much! A+++

A Valuable Idea for Science and Math Teachers.......2007-08-02

Abbott, the author, has the reader imagine three-dimensional structures from a distant horizontal perspective. The third dimension becomes unimportant, and can be dispensed with completely. Taking this further, we are left with a "society" of circles, triangles, and other 2-D geometric figures, all living in Flatland.

As a science and math teacher, I found this book an inspiration for thought-provoking questions, such as: How would you describe the sphere to someone living in Lineland or Flatland? How, for that matter, would you communicate the very concept of thickness to someone living in Flatland? Or volume?

Visualize a sphere crossing Flatland. It starts as a point, then a circle of expanding diameter, then a circle of decreasing diameter, then a point, and then finally nothing. Other 3-D figures can be visualized in comparable manner. The possibilities are endless!

My favorite book to teach.......2007-07-16

This book is such a great tool. I've used it for 10 years and it still gets my students excited about dimensions. They can't believe it was written over one hundred years ago and still, as they say, "blows their minds!"

A Good Book for Looking at the World Differently.......2007-07-05

This book at first is very dense. But once you get used to the writing style it becomes a great tool for thinking about perception. I especially like the section on shading and how that can determine what it is you are looking at. It is a short book but it does take a little a time to get through. Overall, it is a very good book.

Average customer rating:

One of the Better Books
No reason not to own it
Excellent Supporting Book
From my experience with the book
sometimes difficult to read, but the problems are excellent

Classical Dynamics
Donald T. Greenwood
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486696901

Book Description

Graduate-level text for science and technology students provides strong background in the more abstract and intellectually satisfying areas of dynamical theory. Topics include d’Alembert’s principle and the idea of virtual work, Hamilton’s equations, Hamilton-Jacobi theory, canonical transformations, more. Problems and references at chapter ends. 1977 edition.

Customer Reviews:

One of the Better Books.......2006-08-11

I have always enjoyed Greenwood's book and it is much more original than most of the other engineering mechanics books out there. The only real deficiency here is a complete lack of any discussion of motion in a central force or vibrations. This is undoubtably due to the curriculum the book was designed for, but as a book these subjects should have been included for completeness. The absence of these subjects really mars an otherwise outstanding text.

No reason not to own it.......2006-06-21

This is the first book review on the books I listed here that are good for students. The first subject is classical dynamics, in which I listed two books. The book I am gonna review in this post is "Classical Dynamics" by Donald T. Greenwood, Dover Publication.

This is a concise book, whose main text contains 324 pages. Such a small size gives students confidence to read it cover to cover. regarding the mathematical prerequisite, although it claims to be a graduate textbook, it assumes only familiarity with basic calculus and some knowledge in differential equations.

The book is very well organized into seven chapters. The first chapter introduces basic concepts such as generalized coordinates, constraints, virtual work, and so on that are essential and enough for the following chapters. Chapter two derives Lagrange's equations, discusses integrals of motion, and applies the theory to small oscillations. Many interesting examples are worked out in this chapter. Chapter 3 then analyzes four special applications of Lagrange's equations, namely Rayleigh's Dissipation Functions, Impulsive Motion, Gyroscopic Systems, Velocity-Dependent Potentials.

Chapter 4 turns to the other pillar of the theory of classical dynamics: Hamilton's equations. It first elaborates the Hamilton's principle with logical clarity, then derives Hamilton's equations with examples. Finally, it discusses other variational principles and Liouville's theorem.

Chapters 5 and 6 should be considered as a whole. Chapter 5 tells one how to obtain principal functions and characteristic functions by using the Hamilton-Jacobi method. Chapter 6 explores the theory of canonical transformations and its application to dyanamics in more details and in a generalized way, in vewing that a principle function is a generating function for a canonical transformation between two points in phase space. These two chapters contain lots of details that are worth reading carefully.

The last one, Chapter 7 discusses special relativity by applying previously introduced methods. However, I found that such a chapter is actually not very necessary, at least for me. If one did not know much special relativity, he/she would not expect to learn much from this chapter. If one knew special relativity very well, then he/she should simply skip the chapter. But anyway, if you like, it is still fun to read it.

Now, pros and cons. Compared to other polular or standard books on this subject, this book is very well balanced between volume, conciseness, and the amount of details, it is easy to read. The book works every example in a detailed and heuristic way, which are good for the readers to develop their own problem-solving skills. The pictorial illustrations in the book are also very nice. At the end of each chapter, there are a bunch of excercise problems carefully chosen by the author. Final resutls of these problems are given at the end of the book so that readers can check their own answers after working through the solutions by themselves. I found that these problems are extremely usefull and interesting; hence, I solved each of them step by step.

Frankly speaking, I did not find any nonnegligible disadvantage of this book. Someone has a review, saying that "it fails to address issues like how one can use Lagrange's equations (or Hamilton's, for that matter) to correctly account for the effects of nonlinear dissipative forces". But I disagree, because I think topics like nonlinear system should be better treated in a more contemporary method, e.g. in the book: Classical Dynamics: a contemporary approach.

You may feel that the book is a bit too old, since it is first published in 1977. But come on, the subject is Classical dynamics, on which a book can never be too old to read. Another overwhelming reason to own it is that it is priced at only 10.37USD. Can anybody convince me to give up this one and buy the 100USD Goldstein's book instead? No way, of course not.

A slightly different version of this review can be found on my web blog.

Excellent Supporting Book.......2001-09-06

This book is an excellent read, and it explains concepts with unusual clarity. I wouldn't suggest it as a main text, but it is an excellent supplement to others, such as Goldstein or Jose and Saletan. I found this little book explained many concepts far better than these "standards" that are used in most graduate mechanics courses. It includes many nice examples. It also includes the answers to the problems in the back. How often do you see that in a graduate level book? I also think it is an excellent read for physics graduate students, who are just trying to get through the comprehensive exam rather than master the details of classical mechanics.

From my experience with the book.......2000-07-24

Chronologically, "Classical Dynamics" was Donald Greewood's second major publication on Analytical Dynamics, covering more advanced topics than the ones in "Principles of Dynamics," whose first edition preceded "Classical Dynamics" by some 12 years.

"Classical Dynamics" is a somewhat more readable text, but just like its companion book, it fails to address issues like how one can use Lagrange's equations (or Hamilton's, for that matter) to correctly account for the effects of nonlinear dissipative forces. Also, its treatment of velocity-dependent potentials could be substantially extended, as could the chapter on Relativity.

On the other hand, the chapters on variational principles, the Pprinciple of Least Action, Hamilton's mechanics, and, above all, canonical transformations are an absolute "must-read"!

An updated, extended second edition would be most welcome now.

sometimes difficult to read, but the problems are excellent.......1999-11-21

This book can be compared with Walter Rudin's Principles of Mathematical Analysis in that it is very terse and the reader must sit with pencil and paper to fill in many details, both in the theory and example problems. It is the case that this process actively engages the reader into the subject and permits a deeper, fuller understanding than just reading the results and final equations. Having less detail in the theory is understandable, but I've found that the example problems are equally as difficult to follow; this makes it increasingly tough to solve his problems (though once I solve a problem, I feel a great sense of accomplishment) On problems: the problems are very well thought out and complement the theoretical section of the text quite well.

Advanced General Relativity (Cambridge Monographs on Mathematical Physics)

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The only book for advanced GR
Excellent
treasure trove of knowledge

Advanced General Relativity (Cambridge Monographs on Mathematical Physics)
John Stewart
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521449464

Book Description

A modern self-contained introduction to key topics in advanced general relativity. The opening chapter reviews the subject, with strong emphasis on the geometric structures underlying the theory. The next chapter discusses 2-component spinor theory, its usefulness for describing zero-mass fields, its practical application via Newman-Penrose formalism, together with examples and applications. The subsequent chapter is an account of the asymptotic theory far from a strong gravitational source, describing the mathematical theory by which measurements of the far-field and gravitational radiation emanating from a source can be used to describe the source itself. The final chapter describes the natural characteristic initial value problem, first in general terms, and then with particular emphasis for relativity, concluding with its relation to Arnold's singularity theory. Exercises are included.

Customer Reviews:

The only book for advanced GR.......2004-09-18

Although it seems to be a general relativity book, this is actually an excellent book for learning advanced mathematics. The sections on differential geometry and spinor analysis rival any of the dedicated textbooks on these subjects. This is also the only book to give a clear and concise introduction to tetrads and the Newman-Penrose formalism of general relativity.

This book is a must for any serious physicist.

Excellent.......2001-08-20

This is an excellent book (mostly) about the use of spinorial methods in GR. However it is quite difficult, and the author recommends that you try Chandrasekhar or Hawking & Israel first. There is an introductory chapter on the basics of differential geometry which is good but no great shakes, and a lovely short chapter on spinors, Goldman-Sachs, Robinson's theorem, and the NP formalism etc. After that it only gets better. The third chapter is an extraordinarily careful treatment of asymptotics and the fourth is on the *characteristic* initial value problem (ie. on null hypersurfaces---*not* the general cauchy problem!). If you think either of these topics comprises what you've read in MTW, prepare for a surprise!A word of warning, Stewart is a mathematician and it shows. The rigour is splendid---this is real scholarship. The author also edits Clas. & Q. Grav.

treasure trove of knowledge.......2000-05-14

It seems to me that there are far too many in number, and far too few in quality, books on on general relativity.

John Stewart, rather than waste time on the hordes of cute little cartoon models apt for a tourist rather than physicist, gets straight to the heart of the matter and presents amazingly powerful results (on differential geometry/ Spinors/ Asymptopia/Initial Value Problem). He doesn't skip any steps in his proofs and doesn't try to appeal to science fiction intuition.

As someone who hasn't encountered spinors before reading this book, I'm grateful for the helpful appendi on the matter. Unfortuneately however I've found in different books the notation for spinors can vary wildly. The result is that I must refigure out all the basic properties to understand the notation. My complaint is that Stewart doesn't seem* (perhaps it's my ignorance) to use the most common notation, but on the other hand, he also provides the most easily used and referenced appendix.

Book Description

The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, the author uses an algebraic approach which can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics.

The book proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism and general relativity.

The volume is intended for students, researchers and instructors in physics, applied mathematics and engineering interested in this new quaternionic Clifford calculus.

A Broader View of Relativity: General Implications of Lorentz And Poincare Invariance (Advanced Series on Theoretical Physical Science)

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A Broader View of Relativity: General Implications of Lorentz And Poincare Invariance (Advanced Series on Theoretical Physical Science)
Jong-Ping Hsu , and Leonardo Hsu
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 9812566511

Hawking on the Big Bang and Black Holes (Advanced Series in Astrophysics and Cosmology, Vol 8)

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Excellent collection of Hawking's papers on the subject
Excellent collection of Hawking's papers on the subject

Hawking on the Big Bang and Black Holes (Advanced Series in Astrophysics and Cosmology, Vol 8)
Stephen W. Hawking
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 9810210787

Customer Reviews:

Excellent collection of Hawking's papers on the subject.......1999-04-29

This collection of the original papers of one of the pioneers of black hole and big bang theory is an excellent compendium of work on the subject. It shows the development of the theory, along with various co-authors, such as Penrose, Hartle, Gibbons, etc., from 1970 to 1992, during which most of this theory was developed. He discusses various possible quantum states as well as topologies of the universe and their possible outcomes in terms of its evolution in time. Highly technical, for the specialist only, not the general public, as were some of his other books.

Excellent collection of Hawking's papers on the subject.......1999-04-29

Average customer rating:

Tesla, Einstein, Lay: The three pioneers!
Read and understand Einstein!
Explains dark energy!
Great for undergratuated students!
Recommended for beginners!

Advanced Theory of Relativity
Peter Lay
Manufacturer: BookSurge Publishing
ProductGroup: Book
Binding: Paperback

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Book Description

This book explains many aspects of the special theory of relativity with respect to the idea of different space structures in the universe. These structures result because the universe has been developed since its origin till now and its development will go on. New phenomena appear under this consideration. All themes are proved mathematically. The reader only needs a solid knowledge of mathematics up to some basic calculus. Here are some key words:  time dilation  length contraction  mass increase  relativistic Doppler effect  Lorentz transformation  relativistic force  relativistic momentum  kinetic energy  dark energy

Customer Reviews:

Tesla, Einstein, Lay: The three pioneers!.......2006-07-12

It is this great book. I trained on free energy research looking for new information. This book gives new chances of free energy research. Time travel, spacecraft engineering, gravity reduction is possible as relativistic event. Many mathematics but usable for free energy engineers.

Read and understand Einstein!.......2006-06-26

The author gave me a sample of his book for review. Before, Einstein's theory was a mystery for me but now I understand his special theory of relativity and somewhat more. It's a recommendable book.

Explains dark energy!.......2006-06-24

As an astronomer I had to learn too much about phenomena of dark energy. No theory was able to explain it clearly except the author of this book. Dark energy is simply explained as a relativistic effect. This does explain the expanison of the universe. A really good book. Thus 5 stars, if possible I had given 10 stars.

Great for undergratuated students!.......2006-06-24

I am an engineer student and have invested a lot of effort to study the theory of relativity, without satisfying success. Since I read this book I comprehend the basic mathematics of the special theory of relativity. In addition the author describes his advanced theory, also comprehendably, that can explain clearly side-effects appearing when the speed of light changes in several experiments. Thanks Peter for this book!

Recommended for beginners!.......2006-06-22

It was a student who showed me this book. It describes mathematically the basic principle of the special theory of relativity by using a vocabulary of simply understandable words. In a second step the author applies this theory on the already discovered changing of the speed of light that can vary by a factor of up to 4.7 depending on the experimental conditions. This advanced theory can explain some of the strange phenomena occuring in such experiments. I give 5 stars although the advanced theory does only treat the special and not the general theory of relativity.

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