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- As easy as it can be
- As the title says, a good 'First Course'
- Good Intro, but Leaves A LOT out
- Great intro text
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A First Course in General Relativity
Bernard F. Schutz
Manufacturer: Cambridge University Press
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General Relativity
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Introduction to Tensor Calculus, Relativity and Cosmology
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Gravity: An Introduction to Einstein's General Relativity
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ASIN: 0521277035 |
Book Description
General relativity has become one of the central pillars of theoretical physics, with important applications in both astrophysics and high-energy particle physics, and no modern theoretical physicist’s education should be regarded as complete without some study of the subject. This textbook, based on the author’s own undergraduate teaching, develops general relativity and its associated mathematics from a minimum of prerequisites, leading to a physical understanding of the theory in some depth. It reinforces this understanding by making a detailed study of the theory’s most important applications - neutron stars, black holes, gravitational waves, and cosmology - using the most up-to-date astronomical developments. The book is suitable for a one-year course for beginning graduate students or for undergraduates in physics who have studied special relativity, vector calculus, and electrostatics. Graduate students should be able to use the book selectively for half-year courses.
Customer Reviews:
As easy as it can be.......2007-05-22
Nice introduction to GR. Not extensive previous knowledge needed and as clear as it could be.
As the title says, a good 'First Course'.......2007-04-04
There are a lot of books on General Relativity. In approach they vary from no math, to essentially math books. This book is somewhere in the middle. It is said to be suitable for a one year course for beginning graduate students or for undergraduates in physics who have studied special relativity, vector calculus, and electrostatics.
To enable such a student to follow the math in in this book the first part of the book reviews special relativity and vector analysis. Then the book has a section on Tensor Analysis, which was newly developed in Einstein's time when it was called tensor calculus. The treatment of these mathematical concepts in this book are, in my mind, sufficient for a review for a student that had studied them before, but will require some pretty good insight for a student that had not seen them before. This background information covers about a third of the book.
Chapter 5 of the book starts out, 'Until now we have discussed only SR.' The next two thirds cover curvature, physics in a curved spacetime, the Einstein field equations, gravitational radiation (the biggest chapter in the book), and on to the rest of GR.
By the end of the book the student has indeed completed a 'first course' in GR. There is still plenty more to go for the interested student specializing in this area.
Good Intro, but Leaves A LOT out.......2007-02-19
As background, I am a senior undergrad doing a thesis on black hole perturbations (following Chandrasekhar). This was the first book I got on GR, a little over a year ago, and I fell in love with it. It does a great job of quickly, though not completely painlessly, introducing you to GR. HOWEVER, as I now continue my ventures further, I find a lot of fundamental concepts lacking in my education. I went from this book onto parts of Wald: not a good idea IMO. I am currently paging through Lovelock and Rund and wishing the mathematical aspect had been introduced in Schutz as well as here. In the end, very nice, well explained intro to the concepts, but you NEED to either supplement with better mathematical explanation, or move quickly to higher book.
Great intro text.......2007-01-14
I started reading this book at a friend's house about 1 year ago and after graduating and starting to miss physics, I decided to pick it up and try something I didn't get in school. This book does a great job of building a fundamental understand of what is going on(and doesn't shy away from the math). The best part is the different ways it can be read. It is written to leave a lot of the deep math(actually expanding the equations and seeing the results in a more concrete manner) to the reader's discretion. As a working person, this is a huge advantage, as it means I can read ahead to curvature while spending my weekends getting familiar with tensor math.
I highly suggest this as a start for anyone that wants to get a feel for GR(not a pop culture feel, but a real understanding of the ideas and math) but doesn't always have the time to work through the math. I also have the Misner, Thorne and Wheeler book Gravitation, and while it gives a much more expansive study of GR, I don't find myself with the time required to read it.
The only drawback is I feel it doesn't give the best intuition about tensors of a higher order than a one form. But that is probably due to my own lack of intuition in that area.
For clarity, My relevant background in physics and math:
ODE, PDE, Vector Calculus, Introductory Analysis and topology, QM, EM, Mechanics, Optics, Thermodynamics. I've never studied non-euclidean space or any real study of geometry beyond the most basic of real number line topology.
undergraduate book.......2006-12-12
This book helped me survive my first course in general relativity, which I took at a time when I was not prepared to understand the textbook of the course (Wald). I have mixed feelings about the book. On the one hand, I could follow it is as an undergraduate; on the other, the level of the discussion was such that I never really felt like I "got" GR from reading it. Maybe that is the paradox of a low-level book, but for comparison I did not experience this reading, for example, griffiths and jackson. There, I felt like I grasped E&M and one level, and then learned it better at another. Perhaps general relativity doesn't work that way, or perhaps another introductory book is better. I don't really know which.
Book Description
Einstein’s General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a ‘black hole’ in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein’s field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. These conditions are shown to be satisfied in the vicinity of stars of more than twice the solar mass near the endpoint of their nuclear evolution, and in a time-reversed sense for the universe as a whole. In the first case, the singularity in our past. A discussion of the Cauchy problem for General Relativity is also included in the book.
Customer Reviews:
The Large Scale structure of good science books (& spacetime.......2002-02-21
I think that this book has great depth, and is one of the best Stephen Hawking books I have read. My favourite remains 'A Brief History of Time', but still this book is extremely excellent. My compliments to the chef.
A classic in mathematical general relativity.......2002-01-18
This book is now a classic and is written by two giants in mathematics and physics. It wil be used for many years to come and is certainly one of the most widely quoted in the subject.
The authors begin the book by a discussion of the role of gravity in physics and its role as determining the causal structure of the universe. They introduce the idea of a closed trapped surface, setting the stage for the goal of the book, namely the study of the conditions under which a space-time singularity must occur. Black holes and the beginning of the universe are cited as examples of these singularities. The authors also outline briefly the content of each chapter. A neat argument is given for the significance of focal points via the use of Raychaudhari's equation.
The second chapter is an overview of the background in differential geometry needed in the rest of the book. Although complete from an axiomatic point of view, the approach is much too formal for readers who do not have a knowledge of differential geometry. Such a reader should gain the necessary background elsewhere.
General relativity as a theory of gravitation is discussed in chapter 3. Spacetime is assumed to be a connected 4-dimensional smooth manifold on which is defined a Lorentz metric. The topology is assumed to be Hausdorff. Some of the more interesting or well-written parts of this chapter include the example of a spacetime that is not inextendible, the determination of the conformal factor for the spacetime metric, and the discussion of alternative field equations.
The authors discuss the physicial significance of curvature in chapter 4, namely its effect on families of timelike and null curves. The most important part of this chapter is the discussion on certain inequalities tht the energy-momentum tensor should satisfy from a physical viewpoint. These inequalities, called the weak energy condition and the dominant energy condition, allow the authors to prove the existence of singularities in a later chapter. The reader can see clearly the role of the Jacobi equation, and its solution, the Jacobi field, in measuring the separation of nearby geodesics. The existence of conjugate points is proven, and shown to imply the existence of self-intersections in families of geodesics. As a warm-up to showing the non-existence of geodesics of maximal length, the authors employ variational calculus to study how to vary non-spacelike curves connecting points in convex normal neighborhoods in spacetime, and between points and hypersurfaces. In particular, it is shown that a timelike geodesic curve from a hypersurface to a point is maximal iff there is no conjugate point to the hypersurface along the curve. In addition, the authors prove that two points joined by a non-spacelike curve which is not a null geodesic can be joined by a timelike curve.
The authors consider the exact solutions of the Einstein field equations in chapter 5. Most of the "usual" spacetimes are considered, including Minkowski, De Sitter, Anti-de-Sitter, Robertson-Walker, Schwarzschild, Reissner-Nordstrom, Kerr, Taub-Nut, and Godel. The emphasis in on the global properties of the spacetimes and the existence of singularities in them. The famous Penrose diagrams are used to "compactify" spacetimes in order to study their behavior at infinity and their conformal properties. The authors first introduce the concept of a future (past) Cauchy development here, so important in later developments in the book. The reader can see the tools developed in chapter 4 in play here; for example, the existence of a singularity in a spatially homogeneous cosmology is shown to follow directly from the Raychaudhuri equation. The existence of the singularity is proved to be independent of any acceleration or rotation of matter in such cosmologies.
In chapter 5, the authors consider the causal structure of spacetime, namely the study of its conformal geometry. The consideration of the set of all metrics conformal to the physical metric allows one to discuss "geodesic completeness" of spacetime, this concept forming the basis of a later definition of a singularity in spacetime. The more interesting topics discussed in this chapter include the causality conditions (there are no closed non-spacelike curves), and the Alexandrov topology and its connection with the strong causality condition (every neighborhood of a point contains a neighborhood of the point no non-separable curve of which intersects it more than once). When strong causality does hold, the Alexandrov topology is equivalent to the usual manifold topology, and thus the topology of spacetime can be determined by the observation of causal relationships. The discussion on the role of global hyperbolicity in showing the existence of a maximal geodesic is also very well-written.
The next chapter is pretty much independent of the rest, and was put in no doubt for the mathematician who desires to understand the Einstein equations as a set of nonlinear second-order hyperbolic partial differential equations with initial data on a 3-dimensional manifold, the famous Cauchy problem in general relativity.
Chapter 8 is the most important in the book, for its uses the constructions of earlier chapters to define the notion of a singularity in spacetime. The authors argue that singularities are points where physical laws break down and thus to characterize them one attempts to find out whether any such points have been removed, making spacetime "incomplete" in some sense. Such a notion of incompleteness is very meaningful in topological spaces with a positive definite metric, since in that case one can define completeness in terms of the convergence of Cauchy sequences. In spacetimes with a Lorentz metric, the authors discuss the notion of geodesic completeness for null and timelike geodesics. A very detailed treatment of the now famous singularity theorems is given, these theorems involving an inequality of the Ricci tensor. The last two chapters of the book are more physical in nature wherein the singularity problem is shown to have physical relevance via the occurence of black holes at the endpoint of evolution of massive stars.
A wonderful, foundational work of mathematical physics........2000-04-26
The early seventies saw a revolution in cosmology; for the first time, modern mathematical methods were applied to the discipline, with intriguing results. This book was (along with Penrose's articles) the seminal work in global general relativity. Often overlooked is that the first half of Hawking & Ellis is devoted to traditional GR via the tensor calculus, and the q-form conception. However, trying to learn GR with this volume is not recommended (instead, cf. D'Inverno). The meat-and-potatoes of the book is the discussion of gravitational collapse, and the singularity theorems. They provide us with intuitively good reasons for believing in some very strange phenomenon. If you're interested in the frontiers of modern science, and have the appropriate mathematical background, this book cannot be recommended too highly. The little yellow book stands supreme in the hierarchy of works of modern physics.
Suitable only for mathematicians.......1999-10-21
Don't be mislead by Hawking's popular works, this is a book by a mathematician written for mathematicians. Unless you studied mathematics to at least graduate level (you need to understand vector calculus, vector spaces and tensors to get anywhere) you are unlikely to get much from this book. Even then to read it at anything other than the most superficial level is very hard work. However even at the superficial level it gives one insights into some interesting aspects of general relativity.
The best book on modern General Relativity.......1998-07-18
This book of Stephen Hawking is the more elegant one on modern General Relativity and is my favorite book. It covers in brilliant form the gravitational collapse of a star, the theory of black holes, the space-time singularities, the causal structure of space-time, and in its end the initial singularity of the universe, popularly known as the Big Bang. The book is highly mathematical, and is pressuposed that the reader have studied basic abstract algebra and point set topology. But, for the readers highly interested in these subjects(as I am), this is not a obstacle. All theoretical physicists interested in modern General Relativity should have this book, a testimony of the Genius of Stephen Hawking. Definitively, a magnific book.
Amazon.com
A baffling array of science books claim to reveal how the mysteries of the universe have been discovered, but Simon Singh's Big Bang actually delivers on that promise. General readers will find it to be among the very best books dealing with cosmology, because Singh follows the same plan he used in his brilliant Code Book: he puts people--not equations--first in the story. By linking the progression of the Big Bang theory with the scientists who built it up bit by bit, Singh also uncovers an important truth about how such ideas grow.
Death is an essential element in the progress of science, since it takes care of conservative scientists of a previous generation reluctant to let go of an old, fallacious theory and embrace a new and accurate one.
As harsh as this statement seems, even Einstein defended an outmoded idea about the universe when an unknown interloper published equations challenging the great man. Einstein didn't have to die for cosmology to move forward (he reluctantly apologized for being wrong), but stories like this one show how difficult it can sometimes be for new theories to take root. Fred Hoyle, who coined the term "big bang" as a way to ridicule the idea of a universe expanding from some tiny origin point, strongly believed that the cosmos was in a steady state. But Singh shows how Hoyle's research, meant to prove the contrary, added evidence to the expansion model. Big Bang is also a history of astronomical observation, describing the development of new telescopes that were crucial to the development of cosmology. Handwritten summary notes at the end of each long chapter add a charming, classroom feel to this revealing and very readable book. --Therese Littleton
Book Description
A half century ago, a shocking Washington Post headline claimed that the world began in five cataclysmic minutes rather than having existed for all time; a skeptical scientist dubbed the maverick theory the Big Bang. In this amazingly comprehensible history of the universe,
Simon Singh decodes the mystery behind the Big Bang theory, lading us through the development of one of the most extraordinary, important, and awe-inspiring theories in science.
Customer Reviews:
Phenomenally Interesting, Engaging, Stimulating and, Readable.......2007-10-01
For this reader with a lot formal education, but very little of it in the physical sciences, Simon Singh's `Big Bang' was phenomenally interesting, engaging, intellectually stimulating, readable, and educational. Others with more background in cosmology may find it too basic. Singh takes the reader through the history of cosmology as he builds toward an explanation of the Big Bang theory. The opening chapter explains the ancient's earth-centered (and common sensical) view of the universe and its downfall at the hands of Copernicus, Brahe, Kepler and Galileo. Later chapters follow the disproof of ether, Einstein's special and general theories of relativity, and the `great debate' between the supporters of a static universe and Lemaitre and others who supported the idea of an expanding (Big Bang) universe.
A large portion of the book follows the scientific efforts to gather evidence to support one view or the other. The renowned Edwin Hubble and the less so Henrietta Leavitt played key roles in finally providing enough evidence supporting the Big Bang theory to at least make it a credible argument. The remainder of the book follows the debate between the solid state theorists led by Fred Hoyle and the Big Bang backers led first by Gamow and Alpher, but later by others who resolved some of the nagging doubts about the theory, for example, the crucial 1992 proof of tiny variations in cosmic microwave background radiation.
Each chapter (at least in the P.S. version) has handy summary notes. Singh provides a useful glossary as well as recommended further readings for each chapter.
I generally read 50-75 books a year and rate The Big Bang as one of my top five books of the year. Five measly stars don't do it justice. I will resist the temptation to rate as a supernova, but this book greatly enhanced my understanding of the world around us and was a joy to read.
Absolutely the highest recommendation.
Big Bang! Good Book!.......2007-09-28
While I am fascinated by the process of science and how science arrives at theories based on observation, I am also leery about reading books written by scientists. Their knowledge of the area is usually so great that they are unable to reduce the complexity of the subject to that suitable for mere mortals. But Simon Singh with a PhD in particle physics is not one of them. I noted that he had been a producer for the BBC so I felt that there was a chance that he could tell an understandable story. And I was right. This was one of the best science non-fiction books I've read in a long time. Singh walks us through the chronology of the development of the theory, starting with the earliest physicist/astronomers. He gives examples of objections to the Big Bang theory and then shows how the data supports the theory. One of the objections to the theory was that if the theory were true, then there should be background microwave radiation. And he proceeds to tell the story of how this radiation was finally found. Singh also discusses some of the personalities involved in the development from or fight against the theory. All-in-all this was a very worthwhile read, far superior in interest and anecdotes than books like The Elegant Universe or the Physics of the Buffyverse.
Reasonably good cosmology.......2007-08-07
Not much here I haven't seen before, but nicely put together. Certainly a good introduction to the subject, written at a reasonably adult level and very understandable.
The history of Big Bang theory explained.......2007-08-05
Simon Singh is one of my favourite authors when it comes to popular science. I've enjoyed his books a lot, his style is both entertaining and educational at the same time. Big Bang is no different. By focusing his story on the colourful characters instead of equations, Singh makes the book easy to approach.
There's one thing to notice: the book is less about the Big Bang itself and more about the theory of Big Bang. Singh starts from the ancient Greek, describing how the whole concept of science was born and developed. Much of the book is devoted to the argument between Big Bang and steady-state universe theories. After reading this book, the reader will be familiar with the scientific process and the evolution of scientific paradigms.
Another success for Singh, and I'm definitely looking forward to whatever he's doing next. (Review based on the Finnish translation.)
An extremely enjoyable read.......2007-07-21
"Big Bang" is a very informative book which not only elucidates the history of the Big Bang theory, but begins by documenting the history of cosmology in general from many different civilizations, from Pythagoras to Hubble.
Every aspect of the Big Bang theory is discussed from redshift to elemental synthesis, and it is all explained is simple English (well as simple as nuclear physics can get anyway!). The history of modern cosmology is also well documented, discussing Hubble, Hoyle and Lemaitre, to mention just a few. An immense amount of research has been done by Singh for this book, and for this reason I regard it as a vital source for anyone who has a love for science and/or the history of science and cosmology.
An extremely enjoyable read! Highly recommended!
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From SU(3) to Gravity: Festschrift in Honor of Yuval Ne'eman (3 to Gravity : Papers in Honor of Yuval Ne'eman)
Manufacturer: Cambridge University Press
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ASIN: 0521307848 |
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This collection of specially written essays and articles celebrates the sixtieth birthday of Professor Yuval Ne’eman. Professor Ne’eman has been active at the forefront of many areas of modern physics; this book pays tribute to him by reporting and reflecting on the recent developments in these areas. The contributions have been grouped under five main headings: Groups and Gauges; Particles; Science Policy; Astronomy and Astrophysics; Gravity and Supergravity. Within each group are accounts of new work, developments and extensions of established approaches and discussions of current problems and future prospects. The resulting book will be of interest to graduate students and researchers in cosmology and astrophysics, particle theory and relativity, and to all who wish to keep up to date with the interactions and interrelations between these subject areas.
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Approaches to Numerical Relativity
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ASIN: 0521439760 |
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This volume includes contributions by leading workers in the field given at the workshop on Numerical Relativity held in Southampton in December 1991. Numerical Relativity, or the numerical solution of astrophysical problems using powerful computers to solve Einstein’s equations, has grown rapidly over the last 15 years. It is now an important route to understanding the structure of the Universe, and is the only route currently available for approaching certain important astrophysical scenarios. The Southampton meeting was notable for the first full report of the new 2+2 approach and the related null or characteristic approaches, as well as for updates on the established 3+1 approach, including both Newtonian and fully relativistic codes. The contributions range from theoretical (formalisms, existence theorems) to the computational (moving grids, multiquadrics and spectral methods).
Book Description
This text provides a comprehensive and timely introduction to general relativity. The foundations of the theory in Part I are thoroughly developed together with the required mathematical background from differential geometry in Part III. The six chapters in Part II are devoted to tests of general relativity and to many of its applications. Binary pulsars are studied in considerable detail. Much space is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel's proof of his uniqueness theorem, and derivations of the basic laws of black hole physics. The final chapter of this part contains Witten's proof of the positive energy theorem.
The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It is very well structured and should become a standard text for a modern treatment of gravitational physics. The clear presentation of differential geometry makes it also useful for string theory and other fields of physics, classical as well as quantum.
General Relativity
is a complete revision and extension of Straumann's well-known classic textbook "General Relativity and Relativistic Astrophysics."
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Introduction to General Relativistic and Scalar-Tensor Cosmologies
Marcelo Samuel Berman
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ASIN: 1600210139 |
Book Description
Graduate students and researchers in astrophysics and cosmology need a solid grasp of a wide range of physical processes. This authoritative textbook helps readers develop the necessary toolkit of theory. The book is modular in design, allowing the reader to pick and chose a selection of chapters, if necessary. After reviewing the basics of dynamics, electromagnetic theory, and statistical physics, the book carefully develops a solid understanding of radiative processes, spectra, fluid mechanics, plasma physics and MHD, dynamics of gravitating systems, general relativity, nuclear physics, and other key concepts. Throughout, the reader's understanding is developed and tested with problems and helpful hints. This welcome volume provides graduate students with an indispensable introduction to and reference on all the physical processes they will need to successfully tackle cutting-edge research in astrophysics and cosmology. It can be used alone or in conjunction with two companion volumes, which cover stars and stellar systems, and galaxies and cosmology (both forthcoming).
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The Mathematical Theory of Cosmic Strings (Series in High Energy Physics, Cosmology and Gravitation)
M.R. Anderson
Manufacturer: Taylor & Francis
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ASIN: 0750301600 |
Book Description
This book is a comprehensive survey of the current state of knowledge about the dynamics and gravitational properties of cosmic strings treated in the idealized classical approximation as line singularities described by the Nambu-Goto action. The author's purpose is to provide a standard reference to all work that has been published since the mid-1970s and to link this work together in a single conceptual framework and a single notational formalism. A working knowledge of basic general relativity is assumed. The book will be essential reading for researchers and postgraduate students in mathematics, theoretical physics, and astronomy interested in cosmic strings.
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General Relativity, Astrophysics, and Cosmology (Astronomy and Astrophysics Library)
A.K. Raychaudhuri ,
S. Banerji , and
A. Banerjee
Manufacturer: Springer
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ASIN: 038740628X |
Book Description
This book is intended for students interested in the applications of general relativity in astrophysics and cosmology but who would like to avoid mathematical complications. This volume thus combines relativity, astrophysics, and cosmology in a single volume. It provides an introduction to the subject that will enable students to consult more detailed treatises as well as the current literature. For prospective researchers in these fields, the book includes an appendix on differential forms, and an extensive, though not exhaustive list of references. The book is divided into three parts. The section on general relativity gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects. The section on cosmology discusses various cosmological models, observational tests, and scenarios for the early universe.
Customer Reviews:
Who is this book for?.......2007-08-21
For whom was this book written? If you don't know tensor analysis, GR and the rest of that stuff you're sure not going to learn it here. If you do know tensor analysis and the other stuff why are you reading this book?
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