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The Mathematical Theory of Special and General Relativity, by Ashok N Katti
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This book presents the basic theory of relativity in a rational and simplest possible manner, with the emphasis on the Principle of Simplicity in developing the theory. The presentation is in the style of a discussion and is generally devoid of unproven and speculative assertions. In rare cases where speculative ideas are mentioned, they are clearly stated to be such. Test results verifying all of the theoretical results are given and discussed. This work is intended to serve as a resource and reference book for educational purposes. In Parts I and II the principal results of special and general relativity are derived rigorously, discussing the contributions of Einstein, as well as Lorentz, Poincare, Minkowski, Hilbert, Eddington and others, with historical notes touching upon the various aspects of relativity. Multiple derivations are given particularly of the mass-energy relation, the gravitational field equation, and the relativistic orbit of planets. The Schwarzschild metric and its consequences leading to the formation of black holes are treated in detail. The historical problems of physical dilation of time and Einstein's clock paradox are treated in an entirely new manner based upon general relativity. The author has also presented Einstein's gravitational radiation theory, and its application by Peters and Mathews to radiation from orbiting bodies, followed by the study of radiation from a certain binary pulsar by Weisberg and Taylor. These difficult topics are treated without taking shortcuts as is commonly done in textbooks, but in a manner that senior students can understand. A fresh look is taken of Weyl's unification of gravitational and electromagnetic field theories, again a difficult topic avoided by textbooks. The final chapter of Part II is on the elements of field cosmology. Aspects involving particle physics are not covered because they cannot be treated even cursorily in a book of this size dealing primarily with fields; only books specializing in cosmology can do justice to that vast subject. Part III is devoted entirely to tensor calculus, and its application to the geometries of Riemann and Weyl; these are the essential tools of Einstein's and Weyl's theories treated in Part II. Finally, four appendices are provided on certain mathematical topics. Thus the book is self-contained. The book contains 11 figures, an extensive bibliography and an index. Note: (1) Mathematical and other errors corrected March 21, 2015. (2) For earlier versions, a PDF of mathematical errata will be emailed upon request for free. (3) Comments of readers are welcome and may be emailed to ashkatti34@gmail.com.
- Sales Rank: #835861 in Books
- Published on: 2013-04-17
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .68" w x 6.14" l, .94 pounds
- Binding: Paperback
- 300 pages
About the Author
The author was born in India and educated there, and in the UK and USA. He has degrees in mathematical physics and electrical engineering, his last degree being a master's from Virginia Tech. He has worked his entire career in an area spanning physics, mathematics and engineering, dealing with fields and their analytical and numerical evaluation. His professional experience was gained in major establishments in India, UK and USA. He has also taught graduate courses in electromagnetic theory and pure mathematics at Indian and US universities. After retiring from General Electric in the USA he does consulting work, and writes on electromagnetic and gravitational fields, this book being an example of the last mentioned.
Most helpful customer reviews
35 of 38 people found the following review helpful.
Great summary of the subject of Relativity
By Papa Bob
This book by Ashok Katti is a display of his passion for the subject of Relativity. The book is very well written and brings the reader up to date on the history and theory of this complex subject. The mathematics involved in the various theories associated with Relativity have been well organized to be easy for the reader to follow. The end of the book also has a review of the various mathematical proceedures necessary for the serious reader to review in order to study the derivations on most of the equations in the book. An example is the chapter on Tensor Calculus, which is also a subject which Mr. Katti has studied in great depth. This book is highly recommened to the serious physics student and college professors to have in their personal libraries. The book has the potential to be a classic on the subject of Special and General Relativity.
16 of 19 people found the following review helpful.
Special (and some General) Relatvity
By Terry
Great introduction to the mathematics of special relativity -- and some general relativity. for the person looking for an introductory book this has a good mix of the mathematics required.
5 of 6 people found the following review helpful.
Refreshing Take on Relativity
By Jon C
Highly concise and clear, this is definitely a non-traditional, refreshing exposition on relativity. I appreciate the author's choice of language and contents without sacrificing mathematical rigor. Notes on historical development of the theory is a huge plus, and materials are largely self-contained. The use of LaTeX is highly legible, testament to a thoroughly referenced, professional work rarely seen in independent publications.
Compared to a similar publication, 'A Most Incomprehensible Thing' (Collier), I would like the author to expand more on geometrical aspects of the theory, which I think is the best way to tackle the mathematical learning curve of GR. As such this book is geared for the more advanced of the two. I would also like the author to compile a list of all symbols used throughout the book, as well as a more comprehensive index - most of the time I wish to find a concept presented in the book but is missing from it.
The following is a more detailed list of areas I think the book shall be improved upon:
1. Contents can be too concise and terse at times and mathematically demanding despite being self contained.
- Ex. Derivation of the Riemann curvature tensor is rushed through, relying instead on previous definitions and development; calculus of variations needed to understand the chapter or Einstein's and Hilbert's derivations of the field equations.
2. Too focused on mathematical formalism at times. A geometrical approach can be more effective at delivering relativity as a physical theory.
- Ex 1. No spacetime diagram/simultaneity for SR; parallel transport/covariant differentiation presented in an old-fashioned, algebraic way (perhaps to show the original work of Christoffel); no step-by-step visualization for parallel transport about a 'closed loop' when deriving Riemann Curvature Tensor - more advanced Stoke's theorem required instead; no diagrams etc.
- Ex 2. Matrix notation, especially the Jacobian in place of partial derivatives, can be confusing and overcomplicating for those not familiar with it. I contend that it is not necessary for the development in the main text but would be helpful if placed in an appendix.
3. Better organization and categorization is needed. It can be hard to find specific topics for the more experienced reader.
- Ex 1. Newtonian limit of the field equations is put under the chapter "The Schwarzschild Metrics and their Consequences" instead of following immediately the introduction of the field equations.
- Ex 2. Relativistic fluid dynamics (Energy tensor and related) can be grouped into one chapter, instead of loosely dispersed into multiple ones. It is also not as fully developed as, say, Schutz.
4. Miscellaneous: Lack of comprehensive index - a rather serious issue. Providing a list of notations and symbols is encouraged.
I understand the author's emphasis on conciseness and simplicity, but I sincerely hope that he would take most, if not all of them into consideration. These would however not prevent the book from being overall an excellent and passionate work.
On a side note, the book is freshly printed and made on the day of your order, as indicated on the back page. Highly recommended if you have a good background on the core concepts of the theory and basic knowledge of its mathematical formalisms - calculus, vectors, tensors. Bear in mind that this is more of a monograph - you may want additional books, textbooks recommended, to compliment your learning.
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