These lectures will give an extended presentation of General Relativity, that is the relativistic theory of gravitation published by Einstein in 1916. Besides the classical applications ot physics (cosmology, gravitational lensing, black-hole), one will stress the mathematical framework required to formulate the theory in a rigourous way (that is, pseudo-Riemannian differential geometry), as well as some further mathematical developments inspired by theory.
During these lectures, the various elements of differential geometry needed to formulate General Relativity in a rigourous way will be studied. More precisely, one will introduce the notions of connection and curvature on a pseudo-Riemannian manifold. Then Einstein equations will be discussed, as well as some of their solutions. These include the linearized solutions of gravitational waves, and those with spherical symmetry, used to describe the gravitational attraction of spherical objects.
Besides the learning outcomes described in the general section, some more advanced mathematical topics will be studied as well, such as Hawking-Penrose singularity theorem, or some more advanced mathematical technics to solve Einstein equations.
Teaching style: In presence
Mathematical methods for General Relativity
0. Scientific and historical introduction to the theory of General Relativity.
1. Formalism
2. Solutions and applications
3. Advanced topics
"General Relativity", R. M. Wald, The University of Chicago Press (1984).
Ricevimento: On appointment
CLAUDIO BARTOCCI (President)
PIERRE OLIVIER MARTINETTI (President)
NICOLA PINAMONTI (President)
February 27, 2017
MATHEMATICAL METHODS IN GENERAL RELATIVITY
to be defined later
