Special Relativity, Tensors, and Energy Tensor
Author | : Somnath Datta |
Publisher | : |
Total Pages | : 384 |
Release | : 1901 |
Genre | : Continuum mechanics |
ISBN | : 9789811228124 |
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Author | : Somnath Datta |
Publisher | : |
Total Pages | : 384 |
Release | : 1901 |
Genre | : Continuum mechanics |
ISBN | : 9789811228124 |
Author | : Somnath Datta |
Publisher | : World Scientific |
Total Pages | : 384 |
Release | : 2021-03-02 |
Genre | : Science |
ISBN | : 9811228132 |
This book takes the reader from the preliminary ideas of the Special Theory of Relativity (STR) to the doorsteps of the General Theory of Relativity (GTR).The first part explains the main concepts in a layman's language, including STR, the Lorentz transformation, relativistic mechanics. Thereafter the concept of tensors is built up in detail, especially Maxwell's stress tensor with illustrative examples, culminating in the energy-momentum conservation in electromagnetic fields. Mathematical structure of Minkowski's space-time is constructed and explained graphically. The equation of motion is formulated and then illustrated by the example of relativistic rocket. The principle of covariance is explained with the covariant equations of classical electrodynamics. Finally, the book constructs the energy tensor which constitutes the source term in Einstein's field equation, which clears the passage to the GTR.In the book, the concepts of tensors are developed carefully and a large number of numerical examples taken from atomic and nuclear physics. The graphs of important equations are included. This is suitable for studies in classical electrodynamics, modern physics, and relativity.
Author | : Michael Tsamparlis |
Publisher | : Springer Nature |
Total Pages | : 492 |
Release | : |
Genre | : |
ISBN | : 3031317068 |
Author | : Michael Tsamparlis |
Publisher | : Springer Science & Business Media |
Total Pages | : 605 |
Release | : 2010-05-17 |
Genre | : Science |
ISBN | : 3642038379 |
Writing a new book on the classic subject of Special Relativity, on which numerous important physicists have contributed and many books have already been written, can be like adding another epicycle to the Ptolemaic cosmology. Furthermore, it is our belief that if a book has no new elements, but simply repeats what is written in the existing literature, perhaps with a different style, then this is not enough to justify its publication. However, after having spent a number of years, both in class and research with relativity, I have come to the conclusion that there exists a place for a new book. Since it appears that somewhere along the way, mathem- ics may have obscured and prevailed to the degree that we tend to teach relativity (and I believe, theoretical physics) simply using “heavier” mathematics without the inspiration and the mastery of the classic physicists of the last century. Moreover current trends encourage the application of techniques in producing quick results and not tedious conceptual approaches resulting in long-lasting reasoning. On the other hand, physics cannot be done a ́ la carte stripped from philosophy, or, to put it in a simple but dramatic context A building is not an accumulation of stones! As a result of the above, a major aim in the writing of this book has been the distinction between the mathematics of Minkowski space and the physics of r- ativity.
Author | : Anadi Jiban Das |
Publisher | : Springer Science & Business Media |
Total Pages | : 300 |
Release | : 2007-10-05 |
Genre | : Science |
ISBN | : 0387694692 |
Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.
Author | : Alan P. Lightman |
Publisher | : Princeton University Press |
Total Pages | : 616 |
Release | : 2017-09-01 |
Genre | : Science |
ISBN | : 1400889014 |
An essential resource for learning about general relativity and much more, from four leading experts Important and useful to every student of relativity, this book is a unique collection of some 475 problems--with solutions--in the fields of special and general relativity, gravitation, relativistic astrophysics, and cosmology. The problems are expressed in broad physical terms to enhance their pertinence to readers with diverse backgrounds. In their solutions, the authors have attempted to convey a mode of approach to these kinds of problems, revealing procedures that can reduce the labor of calculations while avoiding the pitfall of too much or too powerful formalism. Although well suited for individual use, the volume may also be used with one of the modem textbooks in general relativity.
Author | : Giancarlo Bernacchi |
Publisher | : Lulu.com |
Total Pages | : 302 |
Release | : 2015-06 |
Genre | : Calculus of tensors |
ISBN | : 1326292536 |
-- New MARCH 2021 REVISED RELEASE -- A friendly and non-formal approach to a subject of abstract mathematics that has important applications in physics, especially in General Relativity, but also in other fields. The purpose of the book is mainly didactic and requires some mathematical background (differential calculus, partial derivatives included).
Author | : Derek F. Lawden |
Publisher | : Courier Corporation |
Total Pages | : 224 |
Release | : 2012-03-07 |
Genre | : Science |
ISBN | : 9780486132143 |
This elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult. Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory. Topics include the special principle of relativity and Lorentz transformations; orthogonal transformations and Cartesian tensors; special relativity mechanics and electrodynamics; general tensor calculus and Riemannian space; and the general theory of relativity, including a focus on black holes and gravitational waves. The text concludes with a chapter offering a sound background in applying the principles of general relativity to cosmology. Numerous exercises advance the theoretical developments of the main text, thus enhancing this volume’s appeal to students of applied mathematics and physics at both undergraduate and postgraduate levels. Preface. List of Constants. References. Bibliography.
Author | : Paul Renteln |
Publisher | : Cambridge University Press |
Total Pages | : 343 |
Release | : 2014 |
Genre | : Mathematics |
ISBN | : 1107042194 |
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.
Author | : Günter Ludyk |
Publisher | : Springer Science & Business Media |
Total Pages | : 202 |
Release | : 2013-06-12 |
Genre | : Science |
ISBN | : 3642357989 |
This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einstein's theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.