CODE 61875 ACADEMIC YEAR 2023/2024 CREDITS 6 cfu anno 2 FISICA 9012 (LM-17) - GENOVA 6 cfu anno 1 FISICA 9012 (LM-17) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR FIS/02 TEACHING LOCATION GENOVA SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW The course is part of the first semester of the 1st/2nd year of the Master’s Degree in Physics. It is part of the curriculum of a theoretical physicist. The subject is characterized by an important mathematical structure, which in this course is considered as a necessary tool to deepen the physical contents of General Relativity. AIMS AND CONTENT LEARNING OUTCOMES Exposition of Einstein’s theory of gravitational interactions with its main consequences and applications: black holes (by Schwarzschild, Reisner-Nordström and Kerr), gravitational waves and cosmology. AIMS AND LEARNING OUTCOMES The course provides an introduction to Einstein’s theory of General Relativity. No preliminary mathematical course is required, but only familiarity with covariant formalism and the principles of field theory (action, equations of motion as functional derivatives of action versus fields). The minimum differential geometry tools needed to construct the Einstein-Hilbert action and deduce Einstein equations as field equations will be introduced. The main purpose of the course is to transmit to the student the rich physical content of Einstein’s equations: black holes, gravitational waves and an introduction to cosmology PREREQUISITES No preliminary mathematical course is required, but only familiarity with covariant formalism and the principles of field theory (action, equations of motion as functional derivatives of action with respect to fields) TEACHING METHODS lectures at blackboard (48h) SYLLABUS/CONTENT • Manifolds ◦ Gravity as geometry ◦ What is a manifold? ◦ Vectors again ◦ Tensors again ◦ The metric ◦ An expanding universe ◦ Causality ◦ Tensor densities • Curvature ◦ Overview ◦ Covariant derivatives ◦ Parallel transport and geodesics ◦ Properties of geodesics ◦ The expanding universe revisited ◦ The Riemann curvature tensor ◦ Properties of the Riemann tensor ◦ Symmetries and Killing vectors ◦ Maximally symmetric spaces • Gravitation ◦ Physics in curved spacetime ◦ Einstein’s equation ◦ Lagrangian formulation ◦ Properties of Einstein’s equation ◦ The cosmological constant • The Schwarzschild Solution ◦ The Schwarzschild metric ◦ Birkhoff’s theorem ◦ Singularities ◦ Geodesics of Schwarzschild ◦ Experimental tests ◦ Schwarzschild black holes ◦ Stars and black holes • More General Black Holes ◦ The black hole zoo ◦ Event Horizons ◦ Killing Horizons ◦ Mass, charge, and spin ◦ Charged (Reissner-Nordström) black holes ◦ Rotating (Kerr) black holes • Perturbation Theory and Gravitational Radiation ◦ Linearized theory and gauge transformations ◦ Degrees of freedom ◦ Newtonian fields and photon trajectories ◦ Gravitational wave solutions • Cosmology ◦ maximally symmetric universes ◦ Robertson-Walker metrics ◦ the Friedmann equations ◦ evolution of the scale factor ◦ redshifts and distances ◦ gravitational lensing ◦ our universe ◦ inflation RECOMMENDED READING/BIBLIOGRAPHY Sean M. Carroll: Spacetime and Geometry: An Introduction to General Relativity James B. Hartle: Gravity: An Introduction to Einstein’s General Relativity Ta-Pei Cheng: Relativity, Gravitation and Cosmology: A Basic Introduction TEACHERS AND EXAM BOARD NICOLA MAGGIORE Ricevimento: The reception time is free, by prior telephone or email appointment. Dipartimento di Fisica, via Dodecaneso 33, 16146 Genova piano 7, studio 709 telefono: 010 3536406 email: nicola.maggiore@ge.infn.it Exam Board NICOLA MAGGIORE (President) ANDREA AMORETTI CARLA BIGGIO CAMILLO IMBIMBO SIMONE MARZANI GIOVANNI RIDOLFI PIERANTONIO ZANGHI' LESSONS LESSONS START according to the Manifesto degli Studi Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION There will be an oral examination ASSESSMENT METHODS The oral exam is organized as follows. The student is offered an entry in the course’s lesson log, and is given a few minutes to organize a lesson on the assigned topic lasting about 30 minutes, during which the members of the commission can ask related questions. Exam schedule Data appello Orario Luogo Degree type Note 17/01/2024 09:00 GENOVA Orale 15/02/2024 09:00 GENOVA Orale 11/06/2024 09:00 GENOVA Orale 30/07/2024 09:00 GENOVA Esame su appuntamento 20/09/2024 09:00 GENOVA Esame su appuntamento Agenda 2030 - Sustainable Development Goals Quality education Gender equality