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Department of Mathematics and Applied Mathematics

Department of Mathematics and Applied Mathematics

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  • General Relativity Online Course
    • Overview
    • Tensors and Relativity: Chapter 1
      • Contents
      • Pre- relativistic physics
      • The equations of electromagnetism
      • The principle of Special Relativity
      • Spacetime diagrams and the Lorentz transformations
      • The spacetime interval
      • Minkowski spacetime
      • The null cone
      • Consequences of the Einstein postulates
      • Time dilation
      • Length contraction
      • The twin paradox
      • Velocity composition law
      • Index
      • About this document ...
    • Tensors and Relativity: Chapter 2
      • Contents
      • Four- vectors
      • Four- velocity, momentum and acceleration
      • Relativistic Doppler shift
      • Four- acceleration
      • Relativistic dynamics
      • Example 2.1
      • Example 2.2
      • Index
      • About this document ...
    • Tensors and Relativity: Chapter 3
      • Contents
      • Metrics and forms
      • One- forms
      • Gradients
      • The metric as a mapping of vectors onto one- forms
      • More general tensors
      • Tensors of type 0/2
      • Tensors of type 0/N
      • Tensors of type 2/0
      • Tensors of type M/0
      • Tensors of type M/N
      • Index ``raising'' and ``lowering''
      • General properties of tensors
      • Tensor derivatives and gradients
      • Index
      • About this document ...
    • Tensors and Relativity: Chapter 4
      • Contents
      • The energy- momentum tensor
      • General fluids
      • Conservation of energy- momentum
      • Conservation of particles
      • Perfect fluids
      • The conservation equations
      • The Electromagnetic tensor
      • Index
      • About this document ...
    • Tensors and Relativity: Chapter 5
      • Contents
      • The story so far
      • The gravitational redshift experiment
      • Non- existence of an inertial frame at rest on earth
      • Mass in Newtonian theory
      • The principle of equivalence
      • The principle of equivalence in action
      • Effect of gravity on light
      • Effect of gravity on time
      • Towards spacetime curvature
      • Index
      • About this document ...
    • Tensors and Relativity: Chapter 6
      • Contents
      • Manifolds, tangent spaces and local inertial frames
      • Covariant derivatives and Christoffel symbols
      • Calculating from the metric
      • Tensors in polar coordinates
      • Parallel transport and geodesics
      • The variational method for geodesics
      • The principle of equivalence again
      • The curvature tensor and geodesic deviation
      • The curvature tensor
      • Properties of the Riemann curvature tensor
      • Geodesic deviation
      • The Bianchi identities; Ricci and Einstein tensors
      • The Ricci tensor
      • The Einstein Tensor
      • Index
      • About this document ...
    • Tensors and Relativity: Chapter 7
      • Contents
      • Introduction
      • The non- vacuum field equations
      • The weak field approximation
      • Index
      • About this document ...
    • Tensors and Relativity: Chapter 8
      • Contents
      • The line element
      • The Christoffel symbols
      • The Ricci Tensor
      • The vacuum field equations
      • The Schwarzschild solution
      • General discussion of the Schwartzschild solution
      • Time dilation in a gravitational field
      • Length contraction in a gravitational field
      • Orbits in Schwartzschild spacetime
      • Solution for timelike orbits and precession
      • The bending of light
      • Index
      • About this document ...
    • Tensors and Relativity: Assignment 1
      • Problem
      • About this document ...
      • Hints 1
    • Tensors and Relativity: Assignment 2
      • Problem
      • About this document ...
      • Hints 2
    • Tensors and Relativity: Assignment 3
      • Problem
      • About this document ...
      • Hints 3
    • Tensors and Relativity: Assignment 4
      • Problem
      • About this document ...
      • Hints 4
    • Tensors and Relativity: Assignment 5
      • Problem
      • About this document ...
      • Hints 5
    • Tensors and Relativity: Assignment 6
      • Problem
      • About this document ...
      • Hints 6
    • Tensors and Relativity: Assignment 7
      • Problem
      • About this document ...
      • Hints 7
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Department of Mathematics and Applied Mathematics,
University of Cape Town,
Private Bag X1,
Rondebosch 7701,
South Africa.
Telephone: +27 (0)21-650-3191
Email: Hayley.Leslie@uct.ac.za

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