A Mathematical Journey To Relativity PDF Download
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| Author | : Wladimir-Georges Boskoff |
| Publisher | : Springer Nature |
| Total Pages | : 412 |
| Release | : 2020-06-01 |
| Genre | : Science |
| ISBN | : 3030478947 |
Download A Mathematical Journey to Relativity Book in PDF, ePub and Kindle
This book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.
| Author | : Salvatore Capozziello |
| Publisher | : Springer Nature |
| Total Pages | : 294 |
| Release | : 2021-09-27 |
| Genre | : Science |
| ISBN | : 3030860981 |
Download A Mathematical Journey to Quantum Mechanics Book in PDF, ePub and Kindle
This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the double-split, atomic spectra, and photoelectric effect. The Schrödinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered.The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 self-contained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020.
| Author | : Jose Natario |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 133 |
| Release | : 2011-07-30 |
| Genre | : Science |
| ISBN | : 3642214525 |
Download General Relativity Without Calculus Book in PDF, ePub and Kindle
“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein’s theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.
| Author | : Juan A. Valiente Kroon |
| Publisher | : Cambridge University Press |
| Total Pages | : 627 |
| Release | : 2023-01-31 |
| Genre | : Science |
| ISBN | : 1009291343 |
Download Conformal Methods in General Relativity Book in PDF, ePub and Kindle
This 2016 volume, now reissued as OA, shows how conformal methods can be used to study Einstein's theory of gravity.
| Author | : Wladimir-Georges Boskoff |
| Publisher | : Springer Nature |
| Total Pages | : 556 |
| Release | : |
| Genre | : |
| ISBN | : 303154823X |
Download A Mathematical Journey to Relativity Book in PDF, ePub and Kindle
| Author | : Demetrios Christodoulou |
| Publisher | : European Mathematical Society |
| Total Pages | : 164 |
| Release | : 2008 |
| Genre | : Science |
| ISBN | : 9783037190050 |
Download Mathematical Problems of General Relativity I Book in PDF, ePub and Kindle
General relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newton's theory of gravitation as well as Newton's equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of Gauss' intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler-Lagrange system of partial differential equations. Another method, the study and systematic use of foliations by characteristic (null) hypersurfaces, is in the spirit of Roger Penrose's approach in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media. The book is intended for advanced students and researchers seeking an introduction to the methods and applications of general relativity.
| Author | : James H. Smith |
| Publisher | : Courier Dover Publications |
| Total Pages | : 240 |
| Release | : 2016-03-22 |
| Genre | : Science |
| ISBN | : 0486808963 |
Download Introduction to Special Relativity Book in PDF, ePub and Kindle
By the year 1900, most of physics seemed to be encompassed in the two great theories of Newtonian mechanics and Maxwell's theory of electromagnetism. Unfortunately, there were inconsistencies between the two theories that seemed irreconcilable. Although many physicists struggled with the problem, it took the genius of Einstein to see that the inconsistencies were concerned not merely with mechanics and electromagnetism, but with our most elementary ideas of space and time. In the special theory of relativity, Einstein resolved these difficulties and profoundly altered our conception of the physical universe. Readers looking for a concise, well-written explanation of one of the most important theories in modern physics need search no further than this lucid undergraduate-level text. Replete with examples that make it especially suitable for self-study, the book assumes only a knowledge of algebra. Topics include classical relativity and the relativity postulate, time dilation, the twin paradox, momentum and energy, particles of zero mass, electric and magnetic fields and forces, and more.
| Author | : Masaru Shibata |
| Publisher | : World Scientific |
| Total Pages | : 844 |
| Release | : 2015-11-05 |
| Genre | : Science |
| ISBN | : 981469973X |
Download Numerical Relativity Book in PDF, ePub and Kindle
"This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes."--
| Author | : Hans J. Zweig |
| Publisher | : Edition Steinherz |
| Total Pages | : 140 |
| Release | : 2004 |
| Genre | : Science |
| ISBN | : |
Download Relativity Unraveled Book in PDF, ePub and Kindle
This book presents counterexamples for both Special Relativity and General Relativity Theory. It supports these examples by examining the fallacies and contradictions in Einstein's arguments. it then goes on to derive a new formula for the Doppler effect for light, showing the symmetry of the effect without resorting to Special Relativity. The consquences for cosmology, and for our vision of the universe, are discussed. The meaning of recent data for type 1A supernovae must be reinterpreted. The result is a younger, more compact universe than currently envisioned.
| Author | : Stephen C. Newman |
| Publisher | : John Wiley & Sons |
| Total Pages | : 656 |
| Release | : 2019-07-30 |
| Genre | : Mathematics |
| ISBN | : 1119517532 |
Download Semi-Riemannian Geometry Book in PDF, ePub and Kindle
An introduction to semi-Riemannian geometry as a foundation for general relativity Semi-Riemannian Geometry: The Mathematical Language of General Relativity is an accessible exposition of the mathematics underlying general relativity. The book begins with background on linear and multilinear algebra, general topology, and real analysis. This is followed by material on the classical theory of curves and surfaces, expanded to include both the Lorentz and Euclidean signatures. The remainder of the book is devoted to a discussion of smooth manifolds, smooth manifolds with boundary, smooth manifolds with a connection, semi-Riemannian manifolds, and differential operators, culminating in applications to Maxwell’s equations and the Einstein tensor. Many worked examples and detailed diagrams are provided to aid understanding. This book will appeal especially to physics students wishing to learn more differential geometry than is usually provided in texts on general relativity.
