Introduction and Review of Special Relativity: Inertial frames, Galilean transformation, noninertial frames, Mach’sprinciple, Lorentz transformation and Poincare group, Newtonianmechanics in arbitrary coordinates, electrodynamics.
Riemannian geometry: Space-time as curved manifold, coordinate transformations, tensorcalculus, tetrads and coordinate-free forms, parallel and Fermi-Walkertransport, curvature tensor, Ricci and Weyl tensor, Bianchi Identities, Lie-derivatives, Killing vectors and symmetry, spatial slicing andlocal inertial frames
Physics in curved space times: Particle trajectories, photon trajectories, null coordinates, covariantfield equations, hydrodynamics, thermodynamics, kinetic theory
General Relativity: Principles of equivalence, Einstein field equations, stress-energy, tensor, variational principle, Lagrangian and Hamiltonian formulations,3+1 decomposition, mass and energy, conservation laws, symmetries,asymptotic flatness
Special Solutions: Schwarzschild solution, Kruskal and Penrose diagrams, Resissner-Nordstrom solution, event horizon, black hole, white hole,wormhole, Kerr-Newman solutions, rotating hole and ergosphere, dragging of inertial frames, Lense-Thirring effect, no-hair theorems,singularities, photon and particle orbits, Robertson-Walker metric and Friedmann cosmological models, particle horizon, Kasner metric, gravitational collapse
Tests of General Relativity: Weak fields and PPN formalism, solar system tests, binary pulsar and other tests, GPB
Gravitational radiation: Linearized waves, polarization, generation, g-wave detectors, binary pulsar, LIGO and LISA
All information is representative only, and is likely to change from year to year.