Index - Relativity
A flawed theory of gravity
Christoffel symbols - symmetry
Christoffel symbols and the covariant derivative
Christoffel symbols in terms of the metric tensor
Components of one-forms and vectors
Composition of velocities in relativity
Contravariant tensors
Coordinate transformations - the Jacobian determinant
Covariant and mixed tensors
Covariant derivative of a general tensor
Doppler effect
Doppler effect and four-momentum
Electron-positron collision must produce at least 2 photons
Four-acceleration
Four-momentum conservation
Four-momentum conservation in a spaceship
Four-momentum conservation in the electron-electron collision
Four-momentum conservation in the electron-photon collision
Four-momentum conservation in electron-positron annihilation
Four-momentum of photons
Four-vectors - basics
Four-velocity
Four-velocity - an example
Four-velocity - another example
Geodesic equation and four-velocity
Geodesic equation - 2-d space-time
Geodesic equation in 2-d with exponential metric
Geodesic equation - polar coordinates
Geodesic equation - geodesics on a sphere
Geodesic equation on a paraboloid
Geodesics - paths of longest proper time
Gradient as covector - example in 2-d
Gradient as a one-form
Higher order derivatives are not tensors
Inertia tensor
Invariance of spacetime intervals
Invariant hyperbolas
Length contraction
Linearity of Lorentz transformations
Lorentz invariance of electric charge
Lorentz transformations
Manifolds, curves and surfaces
Metric tensor and basis vectors
Metric tensor for surface of a sphere
Metric tensor in parabolic coordinates
Metric tensor in semi-log coordinates
Metric tensor in sinusoidal coordinates
Metric tensor in spherical coordinates
Metric tensor - inverse and raising and lowering indices
Metric tensor under Lorentz transformation
Momentum and energy
No contraction in directions perpendicular to the motion
Normal vectors and unit normal one-forms
Pole in a barn paradox
Postulates of special relativity
Relativistic units
Spacetime diagrams
Spacetime diagrams - particle detector
Spacetime diagrams - two observers
Spacetime diagrams - events and world lines
Stress-energy tensor - conservation equations
Stress-energy tensor for dust
Stress-energy tensor for a perfect fluid at rest
Stress-energy tensor - symmetry
Symmetric and anti-symmetric tensors
Tensor index notation
Tensor product - numerical example
Tensor trace
Time dilation and proper time
Trace of metric tensor
Transforming derivatives of four-vectors and scalars
Twin paradox
Vectors and the metric tensor