Educational offer - University of Padova

Information on the course unit

Degree course	Second cycle degree in ASTROPHYSICS AND COSMOLOGY SC2490, Degree course structure A.Y. 2019/20, A.Y. 2019/20	bring this page with you
Degree course track	Common track
Number of ECTS credits allocated	6.0
Type of assessment	Mark
Course unit English denomination	GENERAL RELATIVITY
Website of the academic structure	http://astrophysicsandcosmology.scienze.unipd.it/2019/laurea_magistrale
Department of reference	Department of Physics and Astronomy
Mandatory attendance	Sì
Language of instruction	English
Branch	PADOVA
Single Course unit	The Course unit can be attended under the option Single Course unit attendance
Optional Course unit	The Course unit can be chosen as Optional Course unit

Syllabus

Prerequisites:	Knowledge of Special Relativity
Target skills and knowledge:	This course will cover a basic introduction to the theoretical and phenomenological foundations of the General Theory of Relativity. At the end of the course students should be able to master basic techniques to find and analyze solutions to Einstein field equations.
Examination methods:	Questions on the topics presented during the course and solution of a simple / medium problem.
Assessment criteria:	Knowledge and understanding of the course topics. Ability of solving elementary problems related to the course topics.
Course unit contents:	1. Preliminaries Lorentz transformations and addition of velocities in special relativity. The geometry of flat spacetime. Time dilatation, length contraction, and the relativity of simultaneity. Four-vectors and special relativistic kinematics. Special relativistic dynamics and the energy-momentum tensor. Variational principle for Newtonian mechanics and for a free motion in special relativity. Light rays and Doppler shift. Observers and Observations. 2. Space, Time, and Gravity in Newtonian Physics. Inertial frames. The principle of relativity. Newtonian Gravity. Gravitational and Inertial Mass. 3. Gravity as Geometry The equivalence principle. Clocks in a gravitational field and gravitational redshift. Coordinates, line element, and the metric. Light cones and world lines. Length, area, volume computations. Vectors in curved spacetime. Hypersurfaces. Newtonian gravity in spacetime terms (weak field approximation). 4. The Einstein equations Parallel transport and curvature. Covariant derivative, Riemann, Ricci, and Einstein tensor. The source of curvature. Einstein equations and weak field approximation. 5. Geodesics The geodesic equation. Symmetries and Killing vectors. Local inertial frames and freely falling frames. 6. Schwarzschild Geometry Gravitational redshift. Particle orbits: the precession of the perihelion. Light ray orbits: the deflection and time delay of light. Solar system tests of general relativity. 7. Horizons and Coordinate Systems Minkowski spacetime in Rindler coordinates. Schwarzschild black-holes. Eddington-Finkelstein, and Kruskal-Szekeres coordinates, Kruskal and Penrose diagrams. 8. Rotations and Kerr Geometry Geodetic precession around a non-rotating, and a slowly rotating body. Kerr metric and the ergosphere. 9. Cosmology FLRW geometry. Spatial curvature. Evolution in presence of matter, radiation, and a cosmological constant. Cosmological redshift. Luminosity and angular distance. 10 Gravitational waves (if time permits)
Planned learning activities and teaching methods:	Lectures. Weekly assignments.
Textbooks (and optional supplementary readings)	James B. Hartle, Gravity: An Introduction to Einstein's General Relativity. --: Pearson Education (US), --.