type: fundamental courses area: MAT-07

20 h schedule: December 7 h 10-12 / Seminario VIII piano

December 13 h 9-11 / Seminario VIII piano

December 14 h 11-13 / Seminario VIII piano

December 20 h 10-12 / Seminario VIII piano

December 21 h 11-13 / Seminario VIII piano

January 10 h 10-13 / Aula Arzelà

January 11 h 10-13/ Aula Arzelà

January 15 h 10-12/ Aula Arzelà

January 16 h 10-12/ Aula Arzelà

This course covers the basic principles of differential geometry and its application to special and general relativity, some important exact solutions of the Einstein field equations, the singularity theorems, the Cauchy problem in general relativity, and some generalities about (classical) black holes. In detail:

• Short overview of Special Relativity.

• Non-inertial motion and the notion of observer.

• The Equivalence Principle: Newton’s gravity vs. Special Relativity, weak and Einstein’s equivalence principles, physical implications.

• Short review of Differential Geometry, if necessary.

• Postulates of General Relativity.

• Einstein’s field equations: variational derivation;

• Exact solutions & Carter-Penrose diagrams: Minkowski, Schwarzschild, Reissner-Nordstr¨om, Kerr.

• Uniqueness (no-hair) theorems.

• Causality theory on Lorentzian manifolds.

• Singularity theorems: Hawking and Penrose.

• Cauchy problem in General Relativity: Cauchy horizons and loss of predictability

referent: Andrea Mentrelli