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

• Main Authors: Romano, Antonio (Author, http://id.loc.gov/vocabulary/relators/aut), Mango Furnari, Mario (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
• Edition: 1st ed. 2019.
• Subjects: Mathematical physics.; Differential geometry.; Gravitation.; Physics.; Mathematical Physics.; Differential Geometry.; Classical and Quantum Gravitation, Relativity Theory.; Mathematical Methods in Physics.

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...

Table of Contents:

• Preface
• Part I: Elements of Differential Geometry
• 1: Tensor Algebra
• 2: Introduction to Differentiable Manifolds
• 3: Transformation Groups, Exterior Differentiation and Integration
• 4: Absolute Differential Calculus
• Part II: Newtonian Dynamics, Gravitation, and Cosmology
• 5: Recalls of Classical Mechanics and Electrodynamics
• 6: Newtonian Gravitation
• Part III: Special Relativity
• 7: Physical Foundations of Special Relativity
• 8: Special Relativity in Minkowski's Space
• 9: Continuous Systems in Special Relativity
• 10: Electrodynamics in Moving Media
• Part IV: General Relativity and Cosmology
• 11: Introduction to General Relativity
• 12: Linearized Einstein's Equations
• 13: Cauchy's Problem for Einstein's Equations
• 14: Schwarzchild's Universe
• 15: Schwarzchild's Solution and Black-Holes
• 16: Elements of Cosmology
• 17: Relative Formulation of Physical Laws
• Bibliography.