Tensors and Relativity: Chapter 1
- Home
- About Us
- Undergraduate
- Postgraduate
- Staff
- Research
- Research Areas
- Centre for Research in Computational & Applied Mechanics
- Cosmology & Gravity Group
- Laboratory for Discrete Mathematics and Theoretical Computer Science
- Laboratory for Quantum Gravity & Strings
- Marine Resource Assessment & Management Group
- Topology & Algebra Research Group
- National Astrophysics & Space Science Programme (NASSP)
- Rangeland Modelling Group
- Recent Graduates & Theses
- Outreach
- Employment
- Contact Us
- 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
- 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
- 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
- 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
- Tensors and Relativity: Assignment 2
- Tensors and Relativity: Assignment 3
- Tensors and Relativity: Assignment 4
- Tensors and Relativity: Assignment 5
- Tensors and Relativity: Assignment 6
- Tensors and Relativity: Assignment 7
