Class Diary for PHY 6607

 Date       Notes
W 8/23    Classes Begin. Introduction, Administrivia. Conventions, choices.
F 8/25 Spacetime, parametrized curves, proper time
M 8/28 Twin paradox
W 8/30 Energy/momentum, general Lorentz transformation
F 9/1 Lorentz generators
M 9/4 Labor Day (no class)
W 9/6 Lorentz generators as Pauli matrices
F 9/8 Pauli matrix Lorentz transformations,
M 9/11 Boost1 × Boost2 = Boost' × Rotation
W 9/13 Tensor manipulations
F 9/15 Classical field theory from Lagrangian density
M 9/18 Energy momentum tensor, scalar field, perfect fluid
W 9/20 Perfect fluid, relativistic hydrodynamics, first law of thermodynamics
F 9/22 General coordinates, basis vectors, 1-forms, metric. Polar coordinates.
M 9/25 Derivatives of basis vectors, covariant derivative. Laplacian in polar coordinates.
W 9/27 Connection from metric
F 9/29 Commutators, structure constants. Divergence in coordinate frame (useful formula)
M 10/2 Geodesic equation. Connections, geodesics on the sphere
W 10/4 Geodesic equation from extremal path length
F 10/6 Homecoming (no class)
M 10/9 Commutator of covariant derivatives, Riemann curvature tensor. Parallel transport around closed curve.
W 10/11 Geodesic deviation. Symmetries and degrees of freedom of Riemann tensor.
F 10/13 Bianchi identity. Contractions of the Riemann tensor: Ricci tensor, Ricci scalar. Einstein tensor, Weyl tensor.
M 10/16 Geodesic deviation on a sphere. Gravity as geometry: weak equivalence principle. Riemann curvature tensor. Newtonian limit, gravitational redshift.
W 10/18 Towards a relativistic theory of gravity: Scalar potential, conformally flat; Tensor field, General Relativity.
F 10/20 Weak field GR, infinitesimal coordinate transformation, Lorentz gauge.
Bending of light by the sun: γ = 1 − (1.7 ± 4.5) × 10-4 [PRL paper]
M 10/23 Spherical symmetry, Schwarzschild geometry.
W 10/25 Life in Schwarzschild: radial effective potential, r → 0 in τ < π M, Ω² = M/r³
F 10/27 Isotropic coordinates.
M 10/30 Precession of Mercury; binary pulsar, galactic center.
W 11/1 Killing's equation, conserved quantities, Killing vectors on the sphere.
F 11/3 More with Killing vectors, D'Alembertian and Riemann, conserved energy-momentum current density,
M 11/6 Lie derivative
W 11/8 Einstein-Hilbert action, symmetric energy-momentum tensor
F 11/10 Veteran's Day (no class)
M 11/13 Birkhoff's Theorem (uniqueness of Schwarzschild solution).
W 11/15 Spherical symmetry with static sources. Tolman-Oppenheimer-Volkov (TOV) equation.
F 11/17 Constant density solution of TOV equation.
M 11/20 Schwarzschild Riemann components. Gravitational waves, Transverse Traceless gauge.
W 11/22 Constrained Hamiltonian systems.
F 11/24 Thanksgiving (no class)
M 11/27 Gravitational wave sources: quadrupole radiation.
W 11/29 Gravitational radiation: angular distribution, total power.
F 12/1 Effective energy-momentum tensor for gravitational radiation
M 12/4 Gravitational radiation power and strains for astrophysical sources
W 12/6 Last day of class