Core Principles of Special and General Relativity

  • Relativity: A theory of space, time, and gravity
    • THE PRINCIPLE OF RELATIVITY
    • THE LAW OF INERTIA: FOUNDATION OF SPECIAL RELATIVITY
    • SPACE, TIME, AND SPACETIME
    • SPACETIME DIAGRAMS
    • RELATIVITY OF CAUSALITY: SPACELIKE AND TIMELIKE
    • SEGUE TO GENERAL RELATIVITY: NONINERTIAL FRAMES
    • GENERAL RELATIVITY: A THEORY OF GRAVITATION
    • HASTA LA VISTA, GRAVITY
  • Basic special relativity
    • COMPARISON OF TIME INTERVALS: THE BONDI K-FACTOR
    • TIME DILATION
    • VELOCITY ADDITION
    • LORENTZ TRANSFORMATION
    • LENGTH CONTRACTION
    • FOUNDATIONAL EXPERIMENTS
  • Lorentz transformation, I
    • FRAMES IN STANDARD CONFIGURATION
    • FRAMES NOT IN STANDARD CONFIGURATION
    • TRANSFORMATION OF VELOCITY AND ACCELERATION
    • RELATIVISTIC ABERRATION AND DOPPLER EFFECT
  • Geometry of Lorentz invariance
    • LORENTZ TRANSFORMATIONS AS SPACETIME ROTATIONS
    • KINEMATIC EFFECTS FROM THE INVARIANT HYPERBOLA
    • CLASSIFICATION OF LORENTZ TRANSFORMATIONS
    • SPACETIME GEOMETRY AND CAUSALITY
  • Tensors on flat spaces
    • TRANSFORMATION PROPERTIES
    • TENSOR DENSITIES, INVARIANT VOLUME ELEMENT
    • DERIVATIVES OF TENSORS AND THE FOUR-WAVEVECTOR
    • INTERLUDE: DRAW A LINE HERE
    • TENSORS AS MULTILINEAR MAPPINGS
    • METRIC TENSOR REVISITED
    • SYMMETRY OPERATIONS ON TENSORS
    • LEVI-CIVITA TENSOR AND DETERMINANTS
    • PSEUDOTENSORS
    • TOTALLY ANTISYMMETRIC TENSORS
    • INTEGRATION ON MINKOWSKI SPACE
    • THE GHOST OF TENSORS YET TO COME
  • Lorentz transformation, II
  • Particle dynamics
  • Covariant electrodynamics
  • Energy-momentum of fields
  • Relativistic hydrodynamics
  • Equivalence of local gravity and acceleration
  • Acceleration in special relativity
  • Tensors on manifolds
  • Differential geometry
  • General relativity
  • The Schwarzschild metric
  • Physical effects of Schwarzschild spacetime
  • Linearized gravity
  • Relativistic cosmology
  • APPENDIX A  Invariance of the wave equation
  • APPENDIX B  The Doppler effect
  • APPENDIX C  Topics in linear algebra
  • APPENDIX D  Topics in classical mechanics
  • APPENDIX E  Photon and particle orbits