Authors:
- Enriches readers' understanding of general relativity by examining its foundations through an innovative, critical lens
- Employs an integrated approach to the subject by guiding readers through the conceptual transition from classical to relativistic mechanics
- Provides a thorough but accessible introduction to graduate students and researchers interested in obtaining comprehensive understanding of relativity
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Table of contents (18 chapters)
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Front Matter
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Elements of Differential Geometry
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Front Matter
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Newtonian Dynamics, Gravitation, and Cosmology
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Front Matter
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General Relativity and Cosmology
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Front Matter
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About this book
This unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications. The transitions from classical mechanics to special relativity and then to general relativity are explored in detail as well, helping readers to gain a more profound and nuanced understanding of the theory as a whole.
After reviewing the fundamentals of differential geometry and classical mechanics, the text introduces special relativity, first using the physical approach proposed by Einstein and then via Minkowski’s mathematical model. The authors then address the relativistic thermodynamics of continua and electromagnetic fields in matter – topics which are normally covered only very briefly in other treatments – in the next two chapters. The text then turns to a discussion of general relativity by means of the authors’ unique criticalapproach, underlining the difficulty of recognizing the physical meaning of some statements, such as the physical meaning of coordinates and the derivation of physical quantities from those of space-time. Chapters in this section cover the model of space-time proposed by Schwarzschild; black holes; the Friedman equations and the different cosmological models they describe; and the Fermi-Walker derivative.Well-suited for graduate students in physics and mathematics who have a strong foundation in real analysis, classical mechanics, and general physics, this textbook is appropriate for a variety of graduate-level courses that cover topics in relativity. Additionally, it will interest physicists and other researchers who wish to further study the subtleties of these theories and understand the contemporary scholarly discussions surrounding them.
Reviews
“This book is very useful for universities as text book for undergraduate and post graduate students of physics and mathematics. … strongly recommend this book for a textbook in any university.” (P. K. Sahoo, zbMATH 1435.83002, 2020)
Authors and Affiliations
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Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli Federico II, Naples, Italy
Antonio Romano
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Istituto di Cibernetica, Naples, Italy
Mario Mango Furnari
About the authors
Mario Mango Furnari is a senior researcher at Istituto di cibernetica "Edoardo Caianiello."
Bibliographic Information
Book Title: The Physical and Mathematical Foundations of the Theory of Relativity
Book Subtitle: A Critical Analysis
Authors: Antonio Romano, Mario Mango Furnari
DOI: https://doi.org/10.1007/978-3-030-27237-1
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-27236-4Published: 07 October 2019
Softcover ISBN: 978-3-030-27239-5Published: 07 October 2020
eBook ISBN: 978-3-030-27237-1Published: 25 September 2019
Edition Number: 1
Number of Pages: XVI, 496
Number of Illustrations: 46 b/w illustrations, 1 illustrations in colour
Topics: Mathematical Physics, Differential Geometry, Classical and Quantum Gravitation, Relativity Theory, Mathematical Methods in Physics