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The Physical and Mathematical Foundations of the Theory of Relativity

A Critical Analysis

  • Antonio Romano
  • Mario Mango Furnari

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Elements of Differential Geometry

    1. Front Matter
      Pages 1-1
    2. Antonio Romano, Mario Mango Furnari
      Pages 3-38
    3. Antonio Romano, Mario Mango Furnari
      Pages 39-82
    4. Antonio Romano, Mario Mango Furnari
      Pages 83-101
    5. Antonio Romano, Mario Mango Furnari
      Pages 103-128
  3. Newtonian Dynamics, Gravitation, and Cosmology

    1. Front Matter
      Pages 129-129
    2. Antonio Romano, Mario Mango Furnari
      Pages 131-160
    3. Antonio Romano, Mario Mango Furnari
      Pages 161-197
  4. Special Relativity

    1. Front Matter
      Pages 199-199
    2. Antonio Romano, Mario Mango Furnari
      Pages 201-237
    3. Antonio Romano, Mario Mango Furnari
      Pages 239-266
    4. Antonio Romano, Mario Mango Furnari
      Pages 267-291
    5. Antonio Romano, Mario Mango Furnari
      Pages 293-310
  5. General Relativity and Cosmology

    1. Front Matter
      Pages 311-311
    2. Antonio Romano, Mario Mango Furnari
      Pages 313-342
    3. Antonio Romano, Mario Mango Furnari
      Pages 343-359
    4. Antonio Romano, Mario Mango Furnari
      Pages 361-371
    5. Antonio Romano, Mario Mango Furnari
      Pages 373-407
    6. Antonio Romano, Mario Mango Furnari
      Pages 409-429
    7. Antonio Romano, Mario Mango Furnari
      Pages 431-446
    8. Antonio Romano, Mario Mango Furnari
      Pages 447-481
  6. Back Matter
    Pages 483-496

About this book

Introduction

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.

Keywords

Special Relativity General Relativity Equivalence Principle Einstein's Equations Schwarzschild's Solution Fermi-Walker Derivative

Authors and affiliations

  • Antonio Romano
    • 1
  • Mario Mango Furnari
    • 2
  1. 1.Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”Università degli Studi di Napoli Federico IINaplesItaly
  2. 2.Istituto di CiberneticaNaplesItaly

Bibliographic information