Special Relativity Tensors And Energy Tensor
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| 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 | : Somnath Datta |
| Publisher | : |
| Total Pages | : 384 |
| Release | : 1901 |
| Genre | : Continuum mechanics |
| ISBN | : 9789811228124 |
| Author | : Mirjana Dalarsson |
| Publisher | : Academic Press |
| Total Pages | : 276 |
| Release | : 2015-07-08 |
| Genre | : Science |
| ISBN | : 0128034017 |
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that 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 and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in motion, relativistic addition of velocities, and the twin paradox, as well as new material on gravitational waves, amongst other topics. - Clearly combines relativity, astrophysics, and cosmology in a single volume - Extensive introductions to each section are followed by relevant examples and numerous exercises - Presents topics of interest to those researching and studying tensor calculus, the theory of relativity, gravitation, cosmology, quantum cosmology, Robertson-Walker Metrics, curvature tensors, kinematics, black holes, and more - Fully revised and updated with 80 pages of new material on relativistic effects, such as relativity of simultaneity and relativity of the concept of distance, amongst other topics - 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
| Author | : Robert Hermann |
| Publisher | : Math-Sci Press |
| Total Pages | : 132 |
| Release | : 1973 |
| Genre | : Mathematics |
| ISBN | : 9780915692033 |
| Author | : Michael J W Hall |
| Publisher | : Morgan & Claypool Publishers |
| Total Pages | : 159 |
| Release | : 2018-03-23 |
| Genre | : Science |
| ISBN | : 1681748843 |
This book is based on a set of 18 class-tested lectures delivered to fourth-year physics undergraduates at Griffith University in Brisbane, and the book presents new discoveries by the Nobel-prize winning LIGO collaboration. The author begins with a review of special relativity and tensors and then develops the basic elements of general relativity (a beautiful theory that unifies special relativity and gravitation via geometry) with applications to the gravitational deflection of light, global positioning systems, black holes, gravitational waves, and cosmology. The book provides readers with a solid understanding of the underlying physical concepts; an ability to appreciate and in many cases derive important applications of the theory; and a solid grounding for those wishing to pursue their studies further. General Relativity: An Introduction to Black Holes, Gravitational Waves, and Cosmology also connects general relativity with broader topics. There is no doubt that general relativity is an active and exciting field of physics, and this book successfully transmits that excitement to readers.
| 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 | : David Izabel |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2021 |
| Genre | : Science |
| ISBN | : 9782759825738 |
In the first part of this book, the author synthesizes the main results and formulas of physics-Albert Einstein's, with general relativity, gravitational waves involving elastic deformable space-time, quantum field theory, Heisenberg's principle, and Casimir's force implying that a vacuum is not nothingness. In the second part, based on these scientific facts, the author re-studies the fundamental equation of general relativity in a weak gravitational field by unifying it with the theory of elasticity. He considers the Ligo and Virgo interferometers as strain gauges. It follows from this approach that the gravitational constant G, Einstein's constant κ, can be expressed as a function of the physical, mechanical and elastic characteristics of space-time. He overlaps these results and in particular Young's modulus of space-time, with publications obtained by renowned scientists. By imposing to satisfy the set of universal constants G, c, κ, ħ and by taking into account the vacuum data, he proposes a new quantum expression of G which is still compatible with existing serious publications. It appears that time becomes the lapse of time necessary to transmit information from one elastic sheet of space to another. Time also becomes elastic. Thus, space becomes an elastic material, with a particle size of the order of the Planck scale, a new deformable ether, therefore different from the non-existent luminiferous ether. Finally, in the third part, in appendices, the author demonstrates the fundamentals of general relativity, cosmology and the theory of elasticity.
| Author | : Robert M. Wald |
| Publisher | : University of Chicago Press |
| Total Pages | : 507 |
| Release | : 2010-05-15 |
| Genre | : Science |
| ISBN | : 0226870375 |
"Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement "Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today
| Author | : Bertel Laurent |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 203 |
| Release | : 1995-01-16 |
| Genre | : |
| ISBN | : 9814579149 |
The theory of relativity is tackled directly in this book, dispensing with the need to establish the insufficiency of Newtonian mechanics. This book takes advantage from the start of the geometrical nature of the relativity theory. The reader is assumed to be familiar with vector calculus in ordinary three-dimensional Euclidean space.
| Author | : Dwight E. Neuenschwander |
| Publisher | : JHU Press |
| Total Pages | : 244 |
| Release | : 2015 |
| Genre | : Mathematics |
| ISBN | : 142141564X |
It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.--Gary White, editor of The Physics Teacher "American Journal of Physics"
