2016/2017

2016/2017

DM270

FIS/02 (THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS)

DEPARTMENT OF PHYSICS

Fisica teorica

1°

2nd semester (01/03/2017 - 16/06/2017)

6

48 lesson hours

ITALIAN

ORAL TEST

CARFORA MAURO (titolare) - 6 ECTS

MATHEMATICAL METHODS OF THEORETICAL PHYSICS (or an equivalent course in differential geometry); ELETRODYNAMICS & RELATIVITY (or an equivalent course in Special Relativity)

An advanced course in General Relativity and its applications.

Introduction to the Physics of the gravitational field. The weak equivalence principle and the equivalence principle. Local inertial frames, gravitational field and spacetime geometry. Einstein equations. Variational derivation of Einstein equations. The Einstein-Hilbert action. The linearized theory and the Newtonian limit. Gravitational waves in the linearized theory. The Schwarzschild solution: derivation and properties. Test particles in Schwarzschild spacetime. Perihelion shift and deflection of light rays. The Schwarzschild radius. Singularities. Maximal extension of a spacetime. Rindler spacetime. The event horizon. Maximal extension of the Schwarzschild solution and Kruskal spacetime. Event horizons and Black Holes. Conformal compactification and Penrose diagrams. Casual properties of an asymptotically flat spacetime and the characterization of Black Holes. Kerr solution and its properties. Ergosphere and supperradiance. Black hole dynamics. General relativity as a dynamical system. The Arnowitt-Deser-Misner formalism. The Einstein constraints and hyperbolic evolution. Mass and four-momentum of an isolated system. Open problems in mathematical general relativity. Relativistic cosmology. Friedmann equations and cosmological models.

=

Robert M. Wald, General Relativity, The University of Chicago Press

Oral examination.

Oral examination.