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