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

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.