1: SPACE AND TIME

The following sections are included:

• Introduction

• The Hyperbolic Structure of the Space of Relative Velocities

• Relativistic Kinematics on 3-Manifolds

• Class of Inertial Observers and Generalized Lorentz Matrices

• Classical Relativistic Field Dynamics

  • One-dimensional Heat equation

  • One-dimensional Wave equation

  • Gauss-Einstein equations

• Relativistic Field Dynamics on 3-Manifolds

  • Three-dimensional field equations and relationship with Einstein equations

• Flat-Space Solutions

• The de Sitter Solution

• A New Solution of the Vacuum Einstein Field Equations

• A Solution of Mathematical Interest

• The Schwarzschild Solution

  • The Schwarzschild metric

• From Space-Time 4-Metric to 3-Metric and 3-Vector Field

• The Kerr Solution

• The Maxwell Equations References

• References