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Tensors, Relativity, and Cosmology, by Nils Dalarsson MSc - Engineering Physics 1982Licentiate (Swedish degree between MSc and PhD) - Th
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This book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. 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 next section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects. Lastly, the section on cosmology discusses various cosmological models, observational tests, and scenarios for the early universe.
* Clearly combines relativity, astrophysics, and cosmology in a single volume so students can understand more detailed treatises and current literature
* Extensive introductions to each section are followed by relevant examples and numerous exercises
* Provides an easy-to-understand approach to this advanced field of mathematics and modern physics by providing highly detailed derivations of all equations and results
- Sales Rank: #280840 in Books
- Published on: 2005-04-04
- Released on: 2005-03-21
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x .64" w x 6.00" l, 1.30 pounds
- Binding: Paperback
- 320 pages
Review
"…it’s absolutely perfect if you need help with the mathematical aspects of relativity…Many notions from tensor algebra and differential geometry are introduced and explained very clearly, and the main essential formulas are all presented in details."--BookInspections.com, May 27, 2013
About the Author
Nils Dalarsson has been with the Royal Institute of Technology, Department of Theoretical Physics in Stockholm, Sweden, since 1999. His research and teaching experience spans 32 years. Former academic and private sector affiliations include University of Virginia, Uppsala University, FSB Corporation, France Telecom Corporation, Ericsson Corporation, and ABB Corporation. He holds a PhD in Theoretical Physics, an MSc in Engineering Physics, and an MSc in Education.
Mirjana Dalarsson is affiliated with the Research and Development program at Ericsson Corporation. She holds a Licentiate degree in Engineering Physics and has more than 25 years of research and teaching experience. Former affiliations in the academic and private sector include the Royal Institute of Technology, Belgrade University, Uppsala University, and ABB Corporation.
Most helpful customer reviews
28 of 29 people found the following review helpful.
All the Math You Need for GR
By Melissa Anholm
This book, alone, was what got me through my General Relativity course. The text we were using didn't include much math, and the professor didn't want to discuss the mathematical aspects of what we were doing. So I came upon this book armed with a vague physical understanding, but mathematically clueless. Fortunately, this book seems to have been written for precisely such a situation!
In a remarkably clear and concise manner, this book manages to:
- introduce the notations that are commonly used
- demonstrate how a physical system can be represented using the new formalisms
- outline the common mathematical operations that can be performed under this formalism
- describe how these operations are different from similar operations that the reader is already familar with
- show how these mathematical operations are physically relevant to a particular system
The other mathematical texts on this topic all seem to start off slowly with several chapters full of things that, as a physicist, I don't particularly want to know about. This book, by contrast, simply skips right to the parts that are relevant to relativistic calculations, and as a result the reader need not waste time trying to understand mathematical concepts that will not be useful to him.
In short, it's absolutely perfect if you need help with the mathematical aspects of relativity. Its physical explanations are brief, however, so if it's the physical concepts themselves that are troubling you, it might be better to start with a more descriptive book.
11 of 12 people found the following review helpful.
One of the best
By Russell J. Barry
This book starts out with a walk through the gymnastics of manipulating tensor indices's. Tensors can have any number of indices's attached to them. Learning to work with these indices's comes up many times for example in QFT(Quantum Field Theory). It is really basic, but until you see it done a number of time(as in this book) it can be quite confusing. This book teaches you to do this, and does a very good job. This includes the famous Einstein summation convention.
The book also covers co-variant derivatives, which are really important for taking derivatives in curvilinear coordinate since the unit or basis vectors change. Again the book does an excellent job of explaining this. This leads to the next subject of Christoffel Symbols, which come up when taking a co-variant derivative. The book explains these in terms easy to understand.
The book then goes into differential geometry. This is where the book really shines. This section is really a critical part, since you will need the ideas learned here to derive Einstein Field Equations. There is just the right amount of theory here so you can understand what is going on under the hood, but not too so much that you lose all prospective of what is going on.
Then this book covers special relativity. The book really shines here since the approach is a mature one, not watering down the math, but not over doing it either. The book has now taught you about Tensor Analysis, so the author can use it to cover special relativity. A lot of special rel. books do not cover special rel. using this mature approach, they tend to water down the math, but this book has prepared you for it so why not use it.
Also in the Special Rel. sections your Electrodynamic skills will be improved. You are now re-introduced to Maxwell's equations. You might have seen some of the mathematics before in an Electrodynamics course, but this book has given you the math skills you need to really understand it. So now you learn the tensor way to express Maxwell's equations. At this point you start feeling good about your Tensor Analysis skills. You seem to feel the whole universe coming together.
Then the moment you have been reading the book for. The author's start covering General Relativity. As you start reading this part of the book you start feeling good. You are really able to follow what is being done, because the book has done it's job and you have all the background to follow along. Then the most magic moment comes as you are shown how the metric tensor(g) is really the gravitational potential. And now it all comes together and you see how geometry plays a roll in the theory of gravity.
The rest of the book is applications of Einstein's field equations to cosmology. The book also goes into black holes. These are the hardest sections of the book but again the book does such a good job of teaching you what you need, these sections also flow.
In order to get the full benefit from this book you must go through all the steps in the book. In reality most of it is just algebra. I also recommend supplementing this book with Schaum's outline on Tensor Calculus. A lot of people way more knowledgeable in the subject than I am have also recommended this book.
Relativity Demystified is another good book, but it takes a little different approach than this book. It uses Cartan's equations to calculate the Christoffel and Ricci Tensors, but a lot can be learned from doing things a different way. The method called one-forms is really important in learning other subjects. I really recommend Relativity Demystified to get a fuller background for when you read more advanced books. It has typo's and wrong equations in it, but you can find them.
After studying these three books you will be ready to read way more advanced books. These books also give the background required to understand QFT since it requires a very good understanding of Tensors and Relativity. A lot of people have trouble with QFT not because of their Quantum Mechanics skills but because of their lack of Tensor and Relativity skills.
When you are finished you will find General Relativity is not so hard, and there are really only a few ideas behind the whole subject. I always like to supplement textbooks with at least one or two other books. Finding the books that best supplement a books is sometime hard and I have helped you with two in-expensive books.
2 of 2 people found the following review helpful.
The does an excellent job of developing the mathematics associated with these subjects
By Alonzo
The book is mostly mathematics, exactly what it claims to be, with just enough narrative to keep the reader oriented. I completed my second pass through it, this time working through the math in detail with pencil and notepad. The exposition is tractable. The book is self-contained although vector calculus, partial differential equations, and linear algebra are necessary background. There are no problems to solve but after developing the mathematics, Chapter 19 presents the Schwarzschild solution in detail by applying basic results and illustrating how to organize the material to develop solutions. The does an excellent job of developing the mathematics associated with these subjects.
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