The Physical and Mathematical Foundations of the Theory of Relativity : A Critical Analysis / by Antonio Romano, Mario Mango Furnari.

Format:

Book

Author/Creator:

Romano, Antonio.

Series:

Mathematics and Statistics Series

Language:

English

Subjects (All):

Mathematical physics.

Geometry, Differential.

Gravitation.

Mathematical Physics.

Differential Geometry.

Classical and Quantum Gravity.

Mathematical Methods in Physics.

Local Subjects:

Mathematical Physics.

Differential Geometry.

Classical and Quantum Gravity.

Mathematical Methods in Physics.

Physical Description:

1 online resource (948 pages)

Edition:

2nd ed. 2026.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2026.

Summary:

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. This Second Edition includes numerous additions to topics covered in the First Edition, as well as new chapters on the five-dimensional Kaluza-Klein theory, physical coordinate systems and GPS, and a detailed discussion of post-Netwonian theories. 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.

Contents:

Tensor Algebra

Introduction to Differentiable Manifolds

Transformation Groups, Exterior Differentiation and Integration

Absolute Differential Calculus

Review of Classical Mechanics and Electrodynamics

Newtonian Gravitation

Physical Foundations of Special Relativity

Special Relativity in Minkowski's Space

Continuous Systems in Special Relativity

Electrodynamics in Moving Media

Introduction to General Relativity

Linearized Einstein's Equations

Cauchy's Problem for Einstein's Equations

Schwarzchild's Universe

Schwarzchild's Solution and Black-Holes

Elements of Cosmology

Relative Formulation of Physical Laws

About the Gravitational Energy

Physical Coordinate Systems and GPS

Theory of Jordan-Thiry

Post-Newtonian Theories.

Notes:

Print version record.

ISBN:

9783032231796

OCLC:

1611792979