The Physical and Mathematical Foundations of the Theory of Relativity : A Critical Analysis

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 critical approach, 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. Front Matter ....Pages i-xvi Front Matter ....Pages 1-1 Tensor Algebra (Antonio Romano, Mario Mango Furnari)....Pages 3-38 Introduction to Differentiable Manifolds (Antonio Romano, Mario Mango Furnari)....Pages 39-82 Transformation Groups, Exterior Differentiation and Integration (Antonio Romano, Mario Mango Furnari)....Pages 83-101 Absolute Differential Calculus (Antonio Romano, Mario Mango Furnari)....Pages 103-128 Front Matter ....Pages 129-129 Review of Classical Mechanics and Electrodynamics (Antonio Romano, Mario Mango Furnari)....Pages 131-160 Newtonian Gravitation (Antonio Romano, Mario Mango Furnari)....Pages 161-197 Front Matter ....Pages 199-199 Physical Foundations of Special Relativity (Antonio Romano, Mario Mango Furnari)....Pages 201-237 Special Relativity in Minkowski Space (Antonio Romano, Mario Mango Furnari)....Pages 239-266 Continuous Systems in Special Relativity (Antonio Romano, Mario Mango Furnari)....Pages 267-291 Electrodynamics in Moving Media (Antonio Romano, Mario Mango Furnari)....Pages 293-310 Front Matter ....Pages 311-311 Introduction to General Relativity (Antonio Romano, Mario Mango Furnari)....Pages 313-342 Linearized Einstein’s Equations (Antonio Romano, Mario Mango Furnari)....Pages 343-359 Cauchy’s Problem for Einstein’s Equations (Antonio Romano, Mario Mango Furnari)....Pages 361-371 Schwarzschild’s Universe (Antonio Romano, Mario Mango Furnari)....Pages 373-407 Schwarzschild’s Solution and Black Holes (Antonio Romano, Mario Mango Furnari)....Pages 409-429 Elements of Cosmology (Antonio Romano, Mario Mango Furnari)....Pages 431-446 Relative Formulation of Physical Laws (Antonio Romano, Mario Mango Furnari)....Pages 447-481 Correction to: Tensor Algebra (Antonio Romano, Mario Mango Furnari)....Pages C1-C1 Back Matter ....Pages 483-496