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
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.
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.
Book Description
In 1905, Albert Einstein offered a revolutionary theory--special relativity--to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborate to gain objective knowledge of the world. To encompass both the general and special theory, he uses the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.
Customer Reviews:
A great intermediate level book........2007-02-16
We all get an initial taste of relativity in Freshman/Sophomore physics. But where to go next can be a problem. If you like the math accompanying your physics a bit more rigorous than "hand waving", this is a great book. I tried Schutz's book but didn't find the math self contained or rigorous, while trying to jump into Wald's graduate level text on General relativity was way too much to soon. This book strikes a good balance between the physics and the math. Nice coverage of the Lorentz transformation and the invariance of Maxwell's equations under it. Minkowski space time and "hyperbolic" geometry (nice review of hyperbolic functions in analogy with trigonometric functions). And a self contained introduction to differential geometry (as applied to general relativity). I'm finding this great for self study.
Great for learning how to actually use the math behind GR.......2004-07-31
This book is great for teaching the math behind GR using excellent examples from Math and Physics problems (for another great problem solver see also Schaum's Outline of Tensor Calculus, but this has less Physics). It is a bit long winded, spending alot of time on SR and in some place just over the top (for Physicists!), but once through it there should be no problem going to the more advanced texts which deal with more of the uses of GR. At the same level I would also recommend Schutz's First Course in GR, however, Callahan's book goes through and explains the use of the math better, whereas Schutz's is better for uses in GR, surprisingly this is the strength of Callahan's book: you can't really do the Physics properly unless you can do the math! After this it's on to more Physics orientated books like Carroll's excellent Introduction to GR, as a stepping stone to MTW's Gravitation and Wald's GR.
One of the best........2001-08-06
This is one of the best introduction to General Relativity. It is the most accessible introduction to differential geometry. Naturally you have to know calculus, linear algebra, and the basics of special relativity. I bought many books on the subject, and this one belengs to the set I suggest for self-learning.
Disappointing.......2001-04-15
I've only read the first third in detail, but so far this book is frankly disappointing. The treatment is lightweight and padded out with verbiage, some of it oddly off-key. What math or physics student at this level needs (for example) an elementary account of the properties of hyperbolic functions? Spacetime diagrams are drawn with the time axis horizontal, which is something I've never seen in any other relativity text. Okay, it's a minor point, but I found this and similar nonstandard usages a constant irritant. More seriously, the development of relativistic momentum and covariance in chap.3 is quite incoherent, and the definition of 4-velocity is WRONG (at least, by everyone else's standards - it isn't even a 4-vector). There are plenty of exercises, which is good, but no solutions at all - not even outlines - which is not so good.
The book takes over three hundred pages to get to general relativity (where there seems to be no mention of the equivalence principle!), and I doubt if it's worth the effort. You would do better to work through Foster & Nightingale's 'Short Course in General Relativity', which is a first-rate and accessible introduction if you have a little background in special relativity. And it's two-thirds the price.
Conclusion: There may be a good book waiting to be written on these lines, but I'm sorry to say this isn't it. I wouldn't recommend it to anyone as a first course in relativity.
this book.......2001-04-01
At times this book can be confusing, often the author will make something unclear by leaving out a simple sentence or two. I can't really compare it to other texts- although i've looked through many this is the first I tried to actually learn from, but as far as a textbook goes it's not the greatest. In many places once you figure what he's trying to say, you also realize that an added sentence or step or justification would've made it far easier to understand.
Book Description
This textbook is for mathematicians and mathematical physicists and is mainly concerned with the physical justification of both the mathematical framework and the foundations of the theory of general relativity. Previous knowledge of the relevant physics is not assumed. This book is also suitable as an introduction to pseudo-Riemannian geometry with emphasis on geometrical concepts. A significant part of the text is devoted to the discussion of causality and singularity theorems. The insights obtained are applied to black hole astrophysics, thereby making the connection to current active research in mathematical physics and cosmology.
Customer Reviews:
Typing errors.......2003-12-13
I have been reading the 1999 editions and I hoped that new editions have shown up. This book is very concise and clear. However, typing errors occur in ALMOST EVERY PAGE!! When it comes to something that I really do not understand, I have to place brute force in order to figure out if it is typing error or not.
Differential geometry, ralativity, and cosmology together........2000-06-22
This book deals with the physical justification of the mathematical framework involved in the modern and highly sophisticated theories of the structure of the universe.
The book seems to have been written for working physicists and mathematicians, and maybe for graduate students, but I think most of the material of the first 5 chapters could find a place in undergraduate curricula.
There are some other regarded texts treating this same subjects, but this one attempts to ensure that the mathematical description mirrors the physical concepts involved, so this approach also leads to a careful treatment of the structural aspects of mathematics.
The contents are: Local Theory of Space and Time; Analysis on Manifolds; Space and Time from a Global Point of View; Pseudo-Riemannian Manifolds; General Relativity; Robertson-Walker Cosmology; Spherical Symmetry; Causality; Singularity Theorems.
Includes an extensive list of references and a system of guidelines to read the book, because the author states that it is not meant to be read in the same order as it is written.
Very useful as a reference.
Please take a look at the rest of my reviews (just click on my name above).
Average customer rating:
|
Categories, Bundles and Spacetime Topology (Mathematics and Its Applications)
C.T. Dodson
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover
 General
| Science
| Subjects
| Books
General
| Algebra
| Pure Mathematics
| Mathematics
| Science
| Subjects
| Books
General
| Mathematics
| Science
| Subjects
| Books
General Geometry
| Geometry & Topology
| Mathematics
| Science
| Subjects
| Books
Topology
| Geometry & Topology
| Mathematics
| Science
| Subjects
| Books
Mathematical Physics
| Physics
| Science
| Subjects
| Books
General Geometry
| Geometry & Topology
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
Topology
| Geometry & Topology
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
General
| Algebra
| Pure Mathematics
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
Mathematical Physics
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
All Titles
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Professional
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Science
| Qualifying Textbooks - Fall 2007
| Stores
| Books
ASIN: 9027727716 |
Average customer rating:
|
EXOTIC SMOOTHNESS AND PHYSICS: DIFFERENTIAL TOPOLOGY AND SPACETIME MODELS
Torsten Asselmeyer-Maluga , and
Carl H. Brans
Manufacturer: World Scientific Publishing
ProductGroup: Book
Binding: Hardcover
General
| Science
| Subjects
| Books
General
| Mathematics
| Science
| Subjects
| Books
Differential Geometry
| Geometry & Topology
| Mathematics
| Science
| Subjects
| Books
General
| Physics
| Science
| Subjects
| Books
Mathematical Physics
| Physics
| Science
| Subjects
| Books
Differential Geometry
| Geometry & Topology
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
Topology
| Geometry & Topology
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
General
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
Mathematical Physics
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
All Titles
| Qualifying Textbooks - Fall 2007
| Stores
| Books
ASIN: 981024195X |
Average customer rating:
|
Introduction to Relativistic Continuum Mechanics (Lecture Notes in Physics)
Giorgio Ferrarese , and
Donato Bini
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover
General
| Science
| Subjects
| Books
Differential Geometry
| Geometry & Topology
| Mathematics
| Science
| Subjects
| Books
General
| Physics
| Science
| Subjects
| Books
Mathematical Physics
| Physics
| Science
| Subjects
| Books
Thermodynamics
| Dynamics
| Physics
| Science
| Subjects
| Books
Relativity
| Physics
| Science
| Subjects
| Books
Differential Geometry
| Geometry & Topology
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
General
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
Mathematical Physics
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
Relativity
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
ASIN: 3540731660 |
Book Description
This mathematically-oriented introduction takes the point of view that students should become familiar, at an early stage, with the physics of relativistic continua and thermodynamics within the framework of special relativity. Therefore, in addition to standard textbook topics such as relativistic kinematics and vacuum electrodynamics, the reader will be thoroughly introduced to relativistic continuum and fluid mechanics. Emphasis in the presentation is on the 3+1 splitting technique, widely used in general relativity for introducing the relative observers point of view.
Books:
- Statistical Mechanics: A Set of Lectures (Advanced Book Classics)
- Statistics for Social Data Analysis
- String Theory and M-Theory: A Modern Introduction
- Teach Yourself Swahili Complete Course Package (Book + 2CDs) (Teach Yourself Language Complete Courses)
- The Fokker-Planck Equation: Methods of Solutions and Applications (Springer Series in Synergetics)
- The Illustrated Wavelet Transform Handbook
- The Nature of Consciousness : The Structure of Reality: Theory of Everything Equation Revealed : Scientific Verification and Proof of Logic God Is
- The Physics of Basketball
- The Physics of Semiconductors: An Introduction Including Devices and Nanophysics
- The Physics of Solar Cells (Properties of Semiconductor Materials)
Books Index
Books Home
Recommended Books
- Turning Hurts into Halos and Scars into Stars
- The Bearded Dragon Manual
- Second Draft of My Life : A Novel
- Sophie Scholl and the White Rose
- The Adventures of Robin Hood
- Radiation Protection
- The Burning Island: A Journey Through Myth and History in Volcano Country, Hawaii
- An introduction to political economy,
- Overcoming High-Tech Anxiety: Thriving in a Wired World
- Orenburg Oblast Investment & Business Guide
Gravity: An Introduction to Einstein's General Relativity
General Relativity
A First Course in General Relativity
An Introduction to Quantum Field Theory (Frontiers in Physics)
Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics)
