Basic features of differential geometry for Pseudo-Riemannian manifold. Basic Principles of GR. Applications and predictions of Einstein theory.
Learning Objectives
Knowledge acquired: Mathematical skills for GR. Foundations of GR
Competence acquired: Derivation of Einsten Equations. Notable examples of GR solutions
Skills acquired (at the end of the course): Computing geometrical quantities for pseudo-Riemannian manifold. Computing Einstein equations for a given ansatz of the metric
Teaching Methods
6 CFU
Lectures hours: 48
Further information
Office hours Appointment by email: seminara@fi.infn.it
Website: --
Type of Assessment
Oral test
Course program
Mathematical Structures needed to describe a curved space. Geodesics. Gravito-magnetic equations. Clock synchronization. Acceleration and rotation: Fermi coordinates and transport, Tidal forces and measurement of space-time curvature. Geodesic deviation. Killing vectors and conserved quantities. Motion of a test particle in a Schwarzschild metric. RG Test: precession perihelion, deflection of light rays, time delay and red shift. Blak-holes and horizons. Exact field equations for Genera Relativity, Einstein Hilbert action. Gravitational waves,