General Relativity: An Introduction for Physicists

Book Description

After reviewing the basic concept of general relativity, this introduction discusses its mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle.

Relativity: An Introduction to Special and General Relativity

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Good general purpose book on GTR

Relativity: An Introduction to Special and General Relativity
Hans Stephani
Manufacturer: Cambridge University Press
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A First Course in String Theory
Problem Book in Relativity and Gravitation
A First Course in General Relativity
Gravity: An Introduction to Einstein's General Relativity
Exploring Black Holes: Introduction to General Relativity

ASIN: 0521010691

Book Description

Thoroughly revised and updated, this self-contained textbook provides a pedagogical introduction to relativity. It covers the most important features of special as well as general relativity, and considers more difficult topics, such as charged pole-dipole particles, Petrov classification, groups of motions, gravitational lenses, exact solutions and the structure of infinity. The necessary mathematical tools are provided, most derivations are complete, and exercises are included where appropriate. The bibliography lists the original papers and also directs the reader to useful monographs and review papers. Previous Edition Hb(1990): 0-521-37066-3 Previous Edition Pb(1990): 0-521-37941-5

Customer Reviews:

Good general purpose book on GTR.......2005-11-29

I bought this because my copy of Misner Thorne & Wheeler was in a box 1400 miles away, and i wanted to toy around with some ideas in GTR. I needed a good text on GTR, not a watered-down no-math pop-level book, not a specialized research monograph omitting the basics, not a math formulas reference with no more content than an average cheat sheet, but something for those who already are familiar with GTR but lacking any of the usual academic works in their personal library. This book served my purpose perfectly. It comes with some bonuses - a better explanation of Petrov classification than i had seen anywhere else, more on electromagnetics and stress-energy tensors than i was shopping for, and conveniently sized to carry easily about town along with other stuff, something i can't say for the classic MT&W.

I imagine this would be an okay book for someone who doesn't know GTR but has already studied special relativity and is comfortable with senior undergraduate level physics. GTR is by nature a mind-bending subject, and a total newbie may want to get a taste of the main ideas elsewhere. MT&W, in contrast, is full of illustrations, exercises, and other goodies that make it an excellent choice for GTR beginners. Wald's book on General Relativity is another good choice, but my copy of this too is 1400 miles away...

Good features of this book are that it does not loose the physics behind a forest of math, and that it touches on many important areas - gravitational waves, the Kerr metric, tensor maths, cosmology. None in too much depth - but enough to understand the key concepts and see how different areas of general relativity are related. The bibliography seems shortish but appears sufficient for further pursuits. Some areas not covered include alternatives to GTR, string theory, quantization of GTR. Spinors are mentioned briefly; if one is interested in this important topic, Penrose & Rindler should be your destination.

There is no mention of the weak or strong energy conditions in the index. Perhaps these are mentioned somewhere, but the reader wanting to study this vital topic is better off with the book by Wald.

One area that could stand improvement are the exercises. There are exercised, but it would be nice to have more. A student relying on this book alone might end up feeling underexercised, wanting to pump more mental iron elsewhere. More numerical/quantitative exercises to give a feel for how much, how strong are special relativistic and GTR effects in everday and astrophysical applications, would be especially beneficial to this book's usefulness in an undergraduate course context. When used as a reference text, though, such exercises are not important; given my purpose, i am not disappointed.

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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ASIN: 1600210139

An Introduction to Mathematical Cosmology

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Interesting mathematical treatment of topics in cosmology
More of a Review Than an Introduction

An Introduction to Mathematical Cosmology
J. N. Islam
Manufacturer: Cambridge University Press
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Binding: Hardcover

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An Introduction to Modern Cosmology
Principles of Physical Cosmology
Modern Cosmology

ASIN: 0521496500

Book Description

This book provides a concise introduction to the mathematical aspects of the origin, structure and evolution of the universe. The book begins with a brief overview of observational and theoretical cosmology, along with a short introduction of general relativity. It then goes on to discuss Friedmann models, the Hubble constant and deceleration parameter, singularities, the early universe, inflation, quantum cosmology and the distant future of the universe. This new edition contains a rigorous derivation of the Robertson-Walker metric. It also discusses the limits to the parameter space through various theoretical and observational constraints, and presents a new inflationary solution for a sixth degree potential. This book is suitable as a textbook for advanced undergraduates and beginning graduate students. It will also be of interest to cosmologists, astrophysicists, applied mathematicians and mathematical physicists.

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This book provides a concise introduction to the mathematical aspects of the origin, structure and evolution of the universe. The book begins with a brief overview of observational and theoretical cosmology, along with a short introduction to general relativity. It then goes on to discuss Friedmann models, the Hubble constant and deceleration parameter, singularities, the early universe, inflation, quantum cosmology and the distant future of the universe. This new edition contains a rigorous derivation of the Robertson-Walker metric. It also discusses the limits to the parameter space through various theoretical and observational constraints, and presents a new inflationary solution for a sixth degree potential. This book is suitable as a textbook for advanced undergraduates and beginning graduate students. It will also be of interest to cosmologists, astrophysicists, applied mathematicians and mathematical physicists.

Customer Reviews:

Interesting mathematical treatment of topics in cosmology.......2004-12-28

Some books on cosmology specialize in stating the concepts while keeping the mathematics to a minimum. Others state everything in more mathematical terms. Yet others are textbooks which get one to practice the mathematics. This book takes a different approach from any of these.

To understand cosmology, one needs to know some mathematics. And that would be true even if we knew all the answers to our questions. Given that there are actually multiple models of the universe that are being used and debated, it is even more important to see the mathematics that gets used to characterize them.

Still, this is not a textbook with problem sets. It is more of a review text in some areas (particularly general relativity), and a supplementary book in others. It addresses several important topics in cosmology in useful detail.

The book begins with an overview of cosmology and a review of general relativity. Then Islam spends a significant amount of time on the Robertson-Walker metric, with two different derivations of it. Next, we look at Friedman models of the universe. And then, we look at observational cosmology, with estimates and ranges for the Hubble constant and the resulting age of the universe (which hopefully comes out larger than the ages of the stars and galaxies).

After that, Islam discusses models with a cosmological constant. That's a good idea given that in the last few years, we have obtained more and more evidence for the existence of this (or of a dark energy term). He then includes an interesting chapter on singularities.

After this, there are chapters on the early universe. That means the temperature of the early universe and big bang nucleosynthesis. And we find out about the amounts of primordial helium and deuterium (I think these are still very intriguing issues). The author also shows us a variety of inflationary models (I had fun comparing this chapter with what Roger Penrose said about inflation in "The Road to Reality"). Islam then gives a brief account of quantum cosmology, including a mention of the Hartle-Hawking proposal for the wave function of the "ground state" of the universe.

The book concludes with a chapter about the distant future of the universe, including black hole evaporation and proton decay. While such a section may seem speculative and unsophisticated, I think such topics are a genuine part of cosmology.

This is a useful book, and I recommend it as a supplement to almost any cosmology text.

More of a Review Than an Introduction.......2000-11-01

This book presents a review the basics of mathematical cosmology. For example a review of basic general relativity (a co-ordinate approach) is presented early on (Chapter 2). There are no exercises or problems. You could not learn general relativity from this.The discussion of the geometric and kinematic properties of the RW metric were good. Sufficient material is presented for reviews of standard cosmological models in chapters 3 and 5 although the material concerning the relativistic Friedmann models is covered much more clearly in Foster and Nightingale with the same end results and nice do-able exercises.. Chapter five presents a review of models with a cosmological constant.Some exact solutions (original work by the author) are presented. Rather frustratingly, solutions of some equations are presented with no hints at all as to how they are arrived at. Some approximate relationships are stated without suggesting how they are taken.This makes independent study of the book frustrating at times.There are two chapters later on that present the material from the mathematical supplement to Weinberg's 'three minutes' book in more detail. These are quite fun and could be dipped into independently. I bought this book 'hardback at paperback price - 14.95' which was fair. I would not pay the full price for this book - save up and get Weinberg's Gravitation and Cosmology or get it from the library. It is not really suitable for independent study.

An Introduction to String Theory and D-Brane Dynamics

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A little short but does its job.

An Introduction to String Theory and D-Brane Dynamics
Richard J. Szabo
Manufacturer: Imperial College Press
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Binding: Hardcover

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String Theory and M-Theory: A Modern Introduction
D-Branes (Cambridge Monographs on Mathematical Physics)
A First Course in String Theory
Supersymmetry and String Theory: Beyond the Standard Model
String Theory, Vol. 2 (Cambridge Monographs on Mathematical Physics)

ASIN: 1860944272

Book Description

This invaluable book provides a quick introduction to the rudiments of perturbative string theory and a detailed introduction to the more current topic of D-brane dynamics. The presentation is very pedagogical, with much of the technical detail streamlined. The rapid but highly coherent introduction to the subject is perhaps what distinguishes this book from other string theory or D-brane books. The material is based on mini-courses delivered by the author at various summer schools in theoretical high energy physics, so its actual level has been appropriately tested.

Customer Reviews:

A little short but does its job. .......2004-08-01

From a mathematical perspective, string theory, and its modern metamorphosis, M-theory, is the most complex physical theory ever constructed. From a physical and experimental perspective, these theories completely lack any support. Mathematical elegance and the need for a consistent physical theory have driven the research in string theory, and to this day it remains one of the hottest, if not the most esoteric, topics in theoretical physics. Those physicists with a penchant towards mathematics have joined the ranks of those doing research in string theory. Mathematicians are also benefiting immensely from the insights that string theory offers to myriads of concepts and results in mathematics.

This book gives a very quick overview of the main results in string and M-theory, and would be suitable only for those readers who have had a lot of prior exposure to the subject. There are no in-depth explanations given for the physical and mathematical concepts needed in string and M-theories in the book, and therefore it might be difficult for the newcomer curious about these theories to gain an appreciation of them. The mathematics behind these theories is formidable, requiring years of study to digest, and the insight and motivation behind this mathematics is usually not given in the literature, unfortunately.

After a brief discussion of the history of string theory in chapter 1, and also a very brief discussion of the classical dynamics of strings in chapter 2, the author begins a study of how to quantize the bosonic string in chapter 3. This is done using the familiar canonical quantization of quantum field theory but here applied to the (1+1)-dimensional worldsheet field theory. The mass-shell constraints of classical string dynamics appearing as Virasoro operators are subjected to normal ordering in the quantization procedure. The origin of the bosonic critical dimension of spacetime as 26 is not explained in enough detail that will allow the reader to appreciate it. Also discussed, but only briefly, are the `vertex operators', which have become very important recently, especially in mathematics. In this book vertex operators are introduced as an analogy to the operator-state correspondence that is found in ordinary quantum field theory.

Superstring theory is studied in chapter 4, motivated by the need for eliminating tachyonic states and for including fermions in the spectrum. The Ramond-Neveu-Schwarz (RNS) and light-cone Green-Schwarz formalisms are mentioned as two techniques for dealing with superstrings, but the author only uses the RNS formalism in the book. The role of boundary conditions as the origin of the Ramond (R) and Neveu-Schwartz (NS) sectors is explained very well, but the author leaves to the reader (as an exercise) the canonical quantization of the superstring. The origin of the superstring critical dimension as 10 is thus delegated to the reader. The ubiquitous `GSO projection' is introduced as a device for making the theory of interacting strings consistent, one example being the elimination of tachyonic states. The GSO projection is discussed in both the NS and R sectors. The modular invariance of the bosonic string partition function is left as an exercise for the reader. The author does explain well the origin of `spin structures', i.e. their connection with the introduction of fermions, and the consequent use in the superstring theory to get rid of the tachyonic instability. He gives brief discussions of the five different types of string theories, but restricts himself to only Type II superstrings in the remainder of the book. The origin of the famous `T-duality' for closed strings and its relation to the existence of D-branes in superstring theory is explained very well. The author assigns a very interesting exercise for the reader on showing that T-duality interchanges the definition of normal and tangential derivatives, and therefore exchanges Neumann and Dirichlet boundary conditions. This exercise, in this reviewer's opinion, should eliminate sometimes held view of T-duality as being somewhat mysterious. D-branes are explained as being essential for superstring theory, in that there are missing R-R charges in the perturbative string states, i.e. the vertex operators for the R-R states only involve the fields. The D-branes are thus nonperturbative states that carry the R-R charges.

D-branes and their (fascinating) relation to gauge theory are discussed in detail in chapter 6, their dynamics in chapter 7, and their R-R couplings in the last chapter. D-branes are described nonperturbatively, with the massless modes of open strings equated to the fluctuations of D-branes. Massless fields are interpreted as a 10-dimensional gauge theory on the D-brane worldvolume. The guage fields have components as U(1) gauge fields on the D-brane as well as scalar field components that describe the fluctuations of the D-brane. The gauge theory is actually, and most interestingly, a dimensional reduction to the D-brane of supersymmetric Yang-Mills theory. Via a consideration of Wilson lines of the gauge fields, the author shows how T-duality maps gauge fields in open string theory to positions on the D-branes. The dynamics of D-branes is further described in terms of (supersymmetric Yang-Mills) gauge theory, giving the famous AdS/CFT correspondence. This correspondence is quite exciting if one views it from the standpoint of how difficult it is to do nonperturbative calculations in gauge theories. Interactions between D-branes are studied, and the author describes the coincidence (resulting from spacetime supersymmetry) between the D-brane tension and the R-R charge, i.e. that the R-R repulsion between parallel D-branes cancels their gravitational and dilaton attraction. A brief discussion is given of `BPS states' and their relation to D-branes, i.e. that a D-brane is a state that preserves only half of the spacetime supersymmetries. In addition, and similar to the case in gauge field theories where chirality is present, anomalies can arise in D-branes. These arise, as the author shows, on the chiral worldvolume field theory on the intersection of two or more D-branes. Requiring anomaly cancellation will determine completely the coupling between the D-brane and the fields of the R-R sector.

General Relativity: An Introduction to the Theory of Gravitational Field

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No more, no less, just Perfect!!!
A somewhat outdated book
Superb organization and choice of topics.

General Relativity: An Introduction to the Theory of Gravitational Field

Manufacturer: Cambridge University Press
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Book Description

This book is an excellent introduction to the subjects of gravitation and space-time structure. It presumes a good background in special relativity, electrodynamics, and classical mechanics. The book discusses the foundations of Riemannian geometry; the derivation of the Einstein field equations; linearised theory, far fields and gravitational waves; the invariant characterization of exact solutions; gravitational collapse; cosmology; and a final chapter deals with alternative gravitation theories and the problem of quantum gravity. This revised and correct edition brings the experimental evidence up to date. In addition, the sections on quantum gravity have been rewritten and enlarged, and now form a coherent introduction to this subject.

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This nontechnical introduction to the theory of gravitation deals with those parts of the theory that are essential to the beginning student of general relativity, giving all the mathematics necessary for understanding the theory. In this revised second edition, the experimental evidence has been updated and the sections on quantum physics have been rewritten and enlarged. Starting with the foundations of Riemannian geometry and the tensor calculus, the author formulates and works out the essential laws of physics in Riemannian space. Next, the Einstein field equations are derived. All important applications of the theory are dealt with, including issues of current importance, in particular the Schwarzschild metric, gravitational waves, gravitational collapse, black holes and cosmological models. All the associated basic physical problems are fully discussed, but many results that draw heavily on mathematics are given without derivation. The relation to observations and the latest numerical results obtained from them is established.

Customer Reviews:

No more, no less, just Perfect!!!.......2005-07-12

Recently, I have used the book for some topics on GR and Cosmology. The basic Qs you expect from a book are WHY and HOW and this is the only book I came across on GR that answers both Qs. Although the HOW part is very short and examples are few but this book is clear and concise in all its treatments of GR which reflects the clear thinking of the author and his authority on the subject.
There are diagrams and drawing where needed and most important of all is that every chapter includes the references. In combination with a book like Inverno, where the mathematical treatment is extensive, it can be a great self-study combination.

Only the layout of this book is somewhat confusing and I guess that is due to the German translation and the fact that this is actually the compilation of the lectures but anyway it is much better than most of the recent text available on general relativity. Font size is small so it makes this book of 298 pages perhaps equivalent to 400 pages of larger font book. It is one of those books which convey the message clearly in one sentence instead of one page and perfectly suitable for the self-study. By the way I have Wheeler, Rindler, Inverno, Hartle and Dirac and this one I like most when it comes to self-study in limited time.

The chapters are in following order:
1:Introduction.
2:Foundation of Riemannian geometry.
3:Foundation of Einstein's theory of gravitation.
4:Linearised theory of gravitation, far field and gravitational waves.
5:Invariant character of exact solutions.
6:Gravitational collapse and black holes.
7:Cosmology.
8:Non-Einstein theories of gravitation.

A somewhat outdated book.......2000-11-01

This book is fairly complete in its coverage of the field of GR. Most of what one would expect to find is there -- an overview of tensor analysis, physical motivations, the classical solutions to Einstein's field equations, black holes and cosmology, and even some more advanced topics like a brief digression on quantum gravity.

However, the mathematical approach is old-fashioned and boring (for instance, tensors are still defined in terms of their behavior regarding coordinate transformation; no reference to multilinear forms and modern differential geometry). The analytical tools are introduced as a granitic block, somewhat disconnected from the physical reality they will be applied to. The exercises are definitely not inspired: they fail to be oriented towards developing the firm physical intuition and computational skills needed to effectively working out real-life problems -- I mean a researcher's real life, of course :-)

Overall and honestly, Stephani's book resembles works written over half a century ago, to which some notes on advanced topics are appended. Schutz's introductory text "A First Course in General Relativity" and Wald's more ambitious "General Relativity" are much better in all aspects.

Superb organization and choice of topics........1998-10-16

One of the very best texts currently available. Features an excellent choice of topics, superbly organized and clearly presented (well translated from the German original). Particularly strong on algebraic symmetries and invariant classification in addition to the usual topics.

An Introduction to the Science of Cosmology (PBK) (Graduate Series in Astronomy)

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An Introduction to the Science of Cosmology (PBK) (Graduate Series in Astronomy)
Derek Raine , and E.G. Thomas
Manufacturer: Taylor & Francis
ProductGroup: Book
Binding: Paperback

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ASIN: 0750304057

Book Description

A thorough introduction to modern ideas on cosmology and on the physical basis of the general theory of relativity, An Introduction to the Science of Cosmology explores various theories and ideas in big bang cosmology, providing insight into current problems. Assuming no previous knowledge of astronomy or cosmology, this book takes you beyond introductory texts to the point where you are able to read and appreciate the scientific literature, which is broadly referenced in the book. The authors present the standard big bang theory of the universe and provide an introduction to current inflationary cosmology, emphasizing the underlying physics without excessive technical detail. The book treats cosmological models without reliance on prior knowledge of general relativity, the necessary physics being introduced in the text as required. It also covers recent observational evidence pointing to an accelerating expansion of the universe. The first several chapters provide an introduction to the topics discussed later in the book. The next few chapters introduce relativistic cosmology and the classic observational tests. One chapter gives the main results of the hot big bang theory. Next, the book presents the inflationary model and discusses the problem of the origin of structure and the correspondingly more detailed tests of relativistic models. Finally, the book considers some general issues raised by expansion and isotropy. A reference section completes the work by listing essential formulae, symbols, and physical constants. Beyond the level of many elementary books on cosmology, An Introduction to the Science of Cosmology encompasses numerous recent developments and ideas in the area. It provides more detailed coverage than many other titles available, and the inclusion of problems at the end of each chapter aids in self study and makes the book suitable for taught courses.

Quasars and Active Galactic Nuclei: An Introduction

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Quasars and Active Galactic Nuclei: An Introduction
Ajit K. Kembhavi , and Jayant V. Narlikar
Manufacturer: Cambridge University Press
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Galactic Astronomy (Princeton Series in Astrophysics)
Active Galactic Nuclei (Princeton Series in Astrophysics)
Galactic Dynamics (Princeton Series in Astrophysics)
An Introduction to Active Galactic Nuclei

ASIN: 0521479894

Book Description

This book provides an up-to-date and comprehensive account of quasars and active galactic nuclei (AGN). The latest observations and theoretical models are combined in this clear, pedagogic textbook for advanced undergraduates and graduate students. Researchers will also find this wide-ranging and coherent review invaluable. Throughout, detailed derivations of important results are provided to ensure the book is self contained. And theories and models are critically compared with detailed and often puzzling observations from across the spectrum. We are led through all the key topics, including quasar surveys, continuum radiation, time variability, relativistic beaming, accretion disks, jet sidedness, gravitational lensing, unification and detailed, multi-wavelength studies of individual objects. Particular emphasis is placed on radio, X- and gamma-ray observations--not covered in depth in any previous book. All those entering into this exciting and dynamic area of astronomy research will find this book an ideal introduction.

Gravity, Black Holes, and the Very Early Universe: An Introduction to General Relativity and Cosmology

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Gravity, Black Holes, and the Very Early Universe: An Introduction to General Relativity and Cosmology
Tai L. Chow
Manufacturer: Springer
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Binding: Hardcover

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Chow introduces the mathematical methods essential to understanding and applying general relativity--tensor calculus, some differential geometry, etc.--but leaves to more advanced references derivations that a beginning student would likely find overly long and tedious. The book employs standard tensor analysis--which requires only basic calculus for its understanding--and resists the temptation to adopt more powerful mathematical formalisms (like exterior calculus and differential forms) used by researchers in the field. In this way, the student can concentrate on learning physics--and not be distracted by the complexities of unfamiliar mathematical methods.

The book also offers comprehensive discussion of the physics of black holes. The author hits just the right level of presentation: sufficient mathematical detail to demonstrate or make plausible the physical attributes of black holes - in contrast to "hand-waving" discussions found in popularizations of the subject - yet not so much mathematics as to lose track of the physics in an impenetrable forest of equations. An equally strong point is the author's discussion of the most exciting contemporary issues in astrophysics apart from black holes: recent measurements of the cosmic microwave background, the existence of the cosmological constant, dark matter, dark energy and the accelerated expansion of the universe. The final chapters on unification and inflation are also very well done and not generally found in other introductory treatments of general relativity.

In sum, the book is highly informative and has a user-friendly style, which should make it an attractive choice for teachers and students.

Introduction to General Relativity And the Cosmological Constant Problem

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Introduction to General Relativity And the Cosmological Constant Problem
Marcelo Samuel Berman
Manufacturer: Nova Science Publishers
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ASIN: 1594547173

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