Spacetime and Geometry: An Introduction to General Relativity

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.

Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers, Second Edition

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Quantum Mechanics

Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers, Second Edition
David Ferry
Manufacturer: Taylor & Francis
ProductGroup: Book
Binding: Paperback

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ASIN: 0750307250

Book Description

This textbook provides a complete course in quantum mechanics for students of semiconductor device physics and electrical engineering. It provides the necessary background to quantum theory for those starting work on micro- and nanoelectronic structures and is particularly useful for those going on to work with semiconductors and lasers. This book was developed from a course the author has taught for many years with a style and order of presentation of material specifically designed for this audience. It introduces the main concepts of quantum mechanics which are important in everyday solid-state physics and electronics. Each topic includes examples which have been carefully chosen to draw upon relevant experimental research. It also includes problems with solutions to test understanding of theory. For the second edition significant new material has been added to each chapter, providing updated connections with relevant experiments and device concepts. New references and new problems are included.

Customer Reviews:

Quantum Mechanics.......2000-06-10

Intended for introductory undergraduate level in quantum mechanics. Ferry did a thorough job in covering the basics including tunneling and perturbation theory. This book is fairly easy to understand, which make this a good reference good.

An Introduction to Random Vibrations, Spectral & Wavelet Analysis: Third Edition

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Great for a beginner in this area.

An Introduction to Random Vibrations, Spectral & Wavelet Analysis: Third Edition
D. E. Newland
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486442748

Book Description

One of the first engineering books to cover wavelet analysis, this classic text describes and illustrates basic theory, with a detailed explanation of discrete wavelet transforms. It examines joint probability distributions, ensemble averages, and correlation, Fourier analysis, spectral density and excitation response relations for linear systems, more. 1993 edition.

Customer Reviews:

Great for a beginner in this area........2007-01-24

I got it when this one is on sale at $2.99 plus shipping.
So I did not expect much from it; however, after I browsed for a while, it turned out to be one of the great books I own.
It introduces this topic in the straightforward fashion along with good examples and make everything less difficult than supposed to be.

I would recommend this book to any neophyte in this area.
Even not on-sale, only $20 can not be beaten.

Also note that everything in this edition is exactly the same as the hardcover one costing more than $100.

Many-Body Quantum Theory in Condensed Matter Physics: An Introduction (Oxford Graduate Texts)

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EXCELLENT BOOK!

Many-Body Quantum Theory in Condensed Matter Physics: An Introduction (Oxford Graduate Texts)
Henrik Bruus , and Karsten Flensberg
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 0198566336

Book Description

This book is an introduction to the techniques of many-body quantum theory with a large number of applications to condensed matter physics. The basic idea of the book is to provide a self-contained formulation of the theoretical framework without losing mathematical rigor, while at the same time providing physical motivation and examples. The examples are taken from applications in electron systems and transport theory. On the formal side, the book covers an introduction to second quantization, many-body Green's function, finite temperature Feynman diagrams and bosonization. The applications include traditional transport theory in bulk as well as mesoscopic systems, where both the Landau-Buttiker formalism and recent developments in correlated transport phenomena in mesoscopic systems and nano-structures are covered. Other topics include interacting electron gases, plasmons, electron-phonon interactions, superconductivity and a final chapter on one-dimensional systems where a detailed treatment of Luttinger liquid theory and bosonization techniques is given. Having grown out of a set of lecture notes, and containing many pedagogical exercises, this book is designed as a textbook for an advanced undergraduate or graduate course, and is also well suited for self-study.

Customer Reviews:

EXCELLENT BOOK!.......2005-10-21

This book is exactly what a new student (with some training in basic grad courses in solid state, statistical mechanics, etc.) needs to grasp condensed matter physics without a "research-based bias." Todays programs are so focused on application that a thorough treatment of pedigogical materials get superfically taught. Philip Anderson warns about this in his timeless classic "Basic Notions." This book uses QFT in canonical picture (bootstraps), no mention of path integrals. I started out in HEP, so I got trained fairly well in path integrals, some may find this a barrier with the book. Luttinger theory is the most modern topic touched on, applications to materials science. I recommend Wen's book if you want to look at Quantum Hall Effects and Topological Orders (post 1980's).

An Introduction to the Passage of Energetic Particles through Matter

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An Introduction to the Passage of Energetic Particles through Matter
N.J Carron
Manufacturer: Taylor & Francis
ProductGroup: Book
Binding: Hardcover

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ASIN: 0750309350

Book Description

Identifying where to access data, extracting a needed subset from available resources, and knowing how to interpret the format in which data are presented can be time-consuming tasks for scientists and engineers. By collecting all of this information and providing a background in physics, An Introduction to the Passage of Energetic Particles through Matter enables specialists and nonspecialists alike to understand and apply the data. Making modern data more accessible, this book explores the interactions with matter of energetic particles, including photons, electrons, protons, alpha particles, and neutrons. It presents quantities of interest in many applications, such as photon and neutron cross sections, charged particle stopping powers, electron mean ranges, and angular distributions. The book also discusses electron multiple scattering and models for electron mean range against both stopping power and scattering. The author uses numerous graphs throughout the book to illustrate the material and describes the basic physics underlying all processes. The accompanying CD-ROM includes full datasets and large color contour graphs of cross sections, stopping powers, and ranges in all elements at all interesting energies. Compiling information that is scattered throughout the literature, An Introduction to the Passage of Energetic Particles through Matter provides a comprehensive foundation of particle interactions that is of prime importance to many areas of applied physics and supplies an introduction to the massive, invaluable Evaluated Nuclear Data File (ENDF) library.

Introduction to the Physics of Electrons in Solids

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Read this before Ashcroft and Mermin

Introduction to the Physics of Electrons in Solids
Brian K. Tanner
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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Solid State Physics

ASIN: 0521283582

Book Description

In this upper-level text, Professor Tanner introduces the reader to the behavior of electrons in solids, starting with the simplest possible model. Unlike other solid state physics texts, this book does not begin with complex crystallography, but instead builds up from the simplest possible model of a free electron in a box and introduces higher levels of complexity only when the simple model is inadequate. The approach is to introduce the subject through its historical development, and to show how quantum mechanics is necessary for an understanding of the properties of electrons in solids. The author also includes an examination of the consequences of collective behavior in the phenomena of magnetism and superconductivity. Examples and problems are included for practice.

Customer Reviews:

Read this before Ashcroft and Mermin.......2006-01-24

I was a math major as an undergraduate but found myself doing experimental solid state physics in graduate school. I had never had an undergraduate course in solid state and needed something that would allow me to catch up quickly, so I got this book. It is very thin and very accessible. You can read the whole thing and do all the problems in your spare time over the course of a few weeks. Less, if you put your mind to it. The standard textbook for solid state physics, Ashcroft and Mermin, is, in my opinion, a little too long for an introduction if you've never been exposed to the subject before. I'm also not fond of Kittel's undergraduate solid state book. Tanner's is just right. Read this one, then use Ashcroft and Mermin for a reference.

I graduated in 1997 and am teaching now. I recommend Tanner's book to my students, both graduate and undergraduate.

Introduction to Random Vibrations, Spectral and Wavelet Analysis (3rd Edition)

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Good DWT section

Introduction to Random Vibrations, Spectral and Wavelet Analysis (3rd Edition)
D.E. Newland
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Paperback

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ASIN: 0582215846

Book Description

This book is a substantially expanded edition of An Introduction to Random Vibrations and Spectral Analysis which now covers wavelet analysis. Basic theory is thoroughly described and illustrated, with a detailed explanation of how discrete wavelet transforms work. Computer algorithms are expalined and supported by examples and set of problems. An appendix lists 10 computer programs for calculating and displaying wavelet transforms.

Customer Reviews:

Good DWT section.......1999-09-02

I am only interested in the last section which is on DWT. This section is a good introduction to DWT analysis. The basic idea behind the wavelet analysis is expalined fairly good in this sectoin.

Introduction to Solid-State Theory (Springer Series in Solid-State Sciences)

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Introduction to Solid-State Theory (Springer Series in Solid-State Sciences)
Otfried Madelung
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 354060443X

Book Description

Introduction to Solid-State Theory is a textbook for graduate students of physics and materials science. It also provides the theoretical background needed by physicists doing research in pure solid-state physics and its applications to electrical engineering. The fundamentals of solid-state theory are based on a description by delocalized and localized states and - within the concept of delocalized states - by elementary excitations. The development of solid-state theory within the last ten years has shown that by a systematic introduction of these concepts, large parts of the theory can be described in a unified way. This form of description gives a "pictorial" formulation of many elementary processes in solids, which facilitates their understanding.

Solid-State Physics: Introduction to the Theory

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Solid-State Physics: Introduction to the Theory
James D. Patterson , and Bernard C. Bailey
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 3540241159

Book Description

Learning solid state physics involves a certain degree of maturity, since it involves tying together diverse concepts from many areas of physics. The objective is to understand, in a basic way, how solid materials behave. To do this one needs both a good physical and mathematical background. One definition of solid state physics is that it is the study of the physical (e.g. the electrical, dielectric, magnetic, elastic, and thermal) properties of solids in terms of basic physical laws. In one sense, solid state physics is more like chemistry than some other branches of physics because it focuses on common properties of large classes of materials. It is typical that solid state physics emphasizes how physics properties link to electronic structure. We have retained the term solid state physics, even though condensed matter physics is more commonly used. Condensed matter physics includes liquids and non-crystalline solids such as glass, which we shall not discuss in detail. Modern solid state physics came of age in the late thirties and forties, and had its most extensive expansion with the development of the transistor, integrated circuits, and microelectronics. Most of microelectronics, however, is limited to the properties of inhomogeneously doped semiconductors. Solid state physics includes many other areas of course; among the largest of these are ferromagnetic materials, and superconductors. Just a little less than half of all working physicists are in condensed matter.

A course in solid state physics typically begins with three broad areas: (1) How and why atoms bind together to form solids, (2) Lattice vibrations and phonons, and (3) Electrons in solids. One would then typically apply the above to (4) Interactions especially of electrons with phonons, (5) Metals, the Fermi surface and alloys, (6) Semiconductors, (7) Magnetism, (8) Superconductivity, (9) Dielectrics and ferroelectrics, (10) Optical properties, (11) Defects, and (12) Certain other modern topics such as layered materials, quantum Hall effect, mesoscopics, nanophysics, and soft condensed matter. In this book, we will consider all of these.

An Introduction to the Optical Spectroscopy of Inorganic Solids

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An Introduction to the Optical Spectroscopy of Inorganic Solids
Jose Solé , Luisa Bausa , and Daniel Jaque
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Paperback

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ASIN: 0470868864

Book Description

Treats the most basic aspects to be introduced into the field of optical spectroscopy of inorganic materials, enabling a student to interpret simple optical (absorption, reflectivity, emission and scattering) spectra
Contains simple, illustrative examples and solved exercises
Covers the theory, instrumentation and applications of spectroscopy for the characterisation of inorganic materials, including lasers, phosphors and optical materials such as photonics

This is an ideal beginner’s guide for students with some previous knowledge in quantum mechanics and optics, as well as a reference source for professionals or researchers in materials science, especially the growing field of optical materials.

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This practical guide to spectroscopy and inorganic materials meets the demand from academia and the science community for an introductory text that introduces the different optical spectroscopic techniques, used in many laboratories, for material characterisation. Treats the most basic aspects to be introduced into the field of optical spectroscopy of inorganic materials, enabling a student to interpret simple optical (absorption, reflectivity, emission and scattering) spectra Contains simple, illustrative examples and solved exercises Covers the theory, instrumentation and applications of spectroscopy for the characterisation of inorganic materials, including lasers, phosphors and optical materials such as photonics This is an ideal beginner's guide for students with some previous knowledge in quantum mechanics and optics, as well as a reference source for professionals or researchers in materials science, especially the growing field of optical materials.

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