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Unit GENERAL RELATIVITY

Course
Physics Study-unit CodeGP005532CurriculumFisica teoricaTeacherMarta OrselliTeachers
- Marta Orselli - Didattica Ufficiale

Hours
- 42 ore - Didattica Ufficiale - Marta Orselli

CFU6Course RegulationCoorte 2018Offered2018/19Learning activitiesAffine/integrativaAreaAttività formative affini o integrativeSectorFIS/02Type of study-unitOpzionale (Optional)Type of learning activitiesAttività formativa monodisciplinareLanguage of instructionitalianContentsSolutions of Einstein's equations of general relativity and the main physical consequences. Action of the gravitational field and coupling with matter. Conservation laws and symmetries . Energy and conserved charges. Black-holes. Gravitational wavesReference textsS. M. Carroll, Spacetime and Geometry, Addison Wesely (2004).

S. Weinberg, Gravitation and Cosmology, Wiley (1972).Educational objectivesThe main aim of this teaching is to provide students with the bases needed to address and solve the most important problems in General Relativity.

Main knowledge acquired will be:

Knowledge of the principles of general relativity.

Knowledge of solutions of Einstein's equations .

Knowledge of the black hole solutions.

Black hole thermodynamics.

Gravitational waves

The main competence ( ie the ability to apply the acquired knowledge ) will be :

Ability to describe the physical consequences of curved spaces.

Knowing how to discuss symmetries and physical properties of solution of Einstein's equations.PrerequisitesCourse on Introduction to general relativityTeaching methodsface to faceLearning verification modalityOral examExtended programBasic introduction to Einstein's equations; Spherically symmetric metric; Scharzschild metric; Statement of the theorem of Birkhoff; Geodetic time and light-like in Schwarzschild geometry; Deviation of the light rays and the time-delay; Notion of Event Horizon; Kruskal coordinates; the concepts of Black-Hole, singularities and gravitational collapse in general relativity.

Hilbert action. Formulation of the first order. Conservation laws: Symmetries and Killing vectors. ADM formulation of gravity. Hamiltonian formulation of gravity; Asymptotic symmetry and definition of conserved charges; Positivity of 'energy for a gravity system. Energy and momentum of the gravitational field.

Blacks Holes: Geometry and Properties of black holes. Classical thermodynamics of black-holes. Rindler space; elements of causal structure of space-time; Hawking radiation.

Gravitational waves: linearization of Einstein's equations. Quadrupole emission. Emission of a binary system.