Introduction to General Relativity

First part: (~ 16 hrs):
- The equivalence principle;
- Elements of Special Relativity(8+2): inertial observers, Lorentz transformations, the Minkowski metric and the causal structure of the space-time, the Lorentz group, 4-vectors, the Lagrangian of the free particle, covariant formulation of E&M, scatterings and decays;
- General coordinates transformations in flat space-time: the geodetic equation and the
Rindler's metric;
- Classical tests of General Relativity;

Second part (~ 12 hrs)
An introduction to differential geometry: Differential manifolds, tangent and cotangent space, tensor analysis, differential forms, (pseudo-)Riemannian manifolds, linear connections, curvature, geodetic deviation;

Third part (~ 20 hrs) :
- Einstein's Equations: Euristic derivation, Einstein-Hilbert Action, Bianchi Identitities and
diffeomorphisms;
- Conserved quantities in GR: Killing Vectors
- Gravitational waves (GW): Einstein's equations to first order, gauge fixing, propagation of
GW in empy space. Production of GW, the quadrupole formula and the radiated power,
production in binary systems and implications for LIGO/VIRGO and pulsar timing.
- Schwarzschild's solution and black holes: Birkhoff's theorem, physics at the event horizon,
extension beyond the horizon, Kruskal diagram;
- Cosmology (briefly): the FLRW metric and some simple solutions of the cosmological
standard model.

Approximately 8-10 hours will be devoted to solving excercises in classes, either by the students or by myself.