Date | Notes |
M 8/22 | Classes Begin. Introduction, Administrivia. Conventions, choices. |
W 8/24 | Spacetime, parametrized curves, proper time. Twin paradox. 4-velocity, 4-acceleration, energy, momentum. |
F 8/26 | Lorentz transformations. |
M 8/29 | Pauli matrix representation |
W 8/31 | Boost_{1} × Boost_{2} = Boost' × Rotation. Dirac representation. |
F 9/2 | Hurricane Hermine! |
M 9/5 | Labor Day (no class) |
W 9/7 | Tensors |
F 9/9 | T_{(αβγ)}, T_{[αβγ]}, dual, p-forms, exterior derivative, Stokes theorem, "boundary of a boundary vanishes" |
M 9/12 | Scalar field Lagrangian density, functional derivative, vector field Lagrangian. Stress-energy tensor, energy conservation. |
W 9/14 | Stress-energy tensor, perfect fluid, equations of relativistic hydrodynamics. |
F 9/16 | Particle fluid. Relativistic hydrodynamics, number current, first law of thermodynamics. Canonical Maxwell stress tensor. |
M 9/19 | Noether theorem. Spin density, symmetric Maxwell stress tensor. |
W 9/21 | General coordinates, basis vectors, 1-forms, metric. Polar coordinates. |
F 9/23 | Covariant derivative of vector, connection. Covariant derivative of one-form. |
M 9/26 | Covariant derivative of tensor. Connection in terms of metric (and structure constants). |
W 9/28 | Laplacian. Exterior derivative. Parallel transport. Geodesic equation. |
F 9/30 | Parallel transport and geodesics on the sphere. |
M 10/3 | UKansas Colloquium (no class) |
W 10/5 | Parallel transport along a geodesic preserves norm, angles.
Symmetries, Killing vectors, conservation laws.
Commutator of covariant derivatives, Riemann tensor. Symmetries and degrees of freedom. |
F 10/7 | Hurricane Matthew! |
M 10/10 | Curvature and parallel transport around a closed curve. Geodesic deviation. Ricci tensor, Ricci curvature scalar. |
W 10/12 | Locally Minkowski (g = η), freely falling (Γ = 0), frame. Bianchi identity. Einstein tensor. |
F 10/14 | Homecoming (no class) |
M 10/17 | Gravity as geometry, metric and Newtonian potential, gravitational redshift. Scalar Nordström gravity. |
W 10/19 | Tensor Einstein gravity. Weak field, trace reversed, Lorentz gauge. |
F 10/21 | Bending of light in linearized theory and post-Newtonian γ parameter. Spherical symmetry. |
M 10/24 | Schwarzschild solution. Radial effective potential. |
W 10/26 | Kepler, isotropic coordinates, precession in Schwarzschild solution. |
F 10/28 | Precession numbers for Mercury, PSR 1913+16, S2. |
M 10/31 | Killing vectors R, S,T. Killing vector identities. |
W 11/2 | Lie derivative. Schwarzschild revisited. |
F 11/4 | Penrose diagram. Birkhoff's theorem (uniqueness of Schwarzschild solution). Sources. TOV equation. |
M 11/7 | Constant density relativistic star. Degenerate Fermi star. |
W 11/9 | Weak field gravitational waves. TT gauge. "Plus" and "cross" polarizations. |
F 11/11 | Veteran's Day (no class) |
M 11/14 | Gravitational wave energy-momentum. Sources, quadrupole term. |
W 11/16 | Quadrupole angular distribution, radiated power. Coalescence of two 30 solar mass black holes at 70 billion light years distance. |
F 11/18 | Einstein-Hilbert action. |
M 11/21 | Einstein Hilbert action. Energy momentum tensor source. Charged (Reissner Nordström) black ho,e |
W 11/23–F 11/25 | Thanksgiving (no class) |
M 11/28 | Rotating black hole, surface gravity, temperature, area theorem, entropy, thermodynamics. Hawking radiation. |
W 11/30 | Black hole evaporation. No hair. Extra dimensions. |
F 12/2 | Extrinsic curvature. |
M 12/5 | Gauss-Codazzi equations. |
W 12/7 | Last day of class. GPS. |