| First cycle degree courses | Second cycle degree courses | Single cycle degree courses |
| School of Science | ||
| ASTROPHYSICS AND COSMOLOGY | ||
Course unit
GENERAL RELATIVITY
SCP7081661, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
GENERAL RELATIVITY
SCP7081661, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
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 |
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|---|---|---|
| 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 | |
| E-Learning website | https://elearning.unipd.it/dfa/course/view.php?idnumber=2019-SC2490-000ZZ-2019-SCP7081661-N0 | |
| 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 |
Lecturers
| Teacher in charge | MARCO PELOSO | FIS/02 |
|---|
Mutuated
| Course unit code | Course unit name | Teacher in charge | Degree course code |
|---|---|---|---|
| SCP7081661 | GENERAL RELATIVITY | MARCO PELOSO | SC2443 |
ECTS: details
| Type | Scientific-Disciplinary Sector | Credits allocated | |
|---|---|---|---|
| Core courses | FIS/02 | Theoretical Physics, Mathematical Models and Methods | 6.0 |
Course unit organization
| Period | First semester |
|---|---|
| Year | 1st Year |
| Teaching method | frontal |
| Type of hours | Credits | Teaching hours |
Hours of Individual study |
Shifts |
|---|---|---|---|---|
| Lecture | 6.0 | 48 | 102.0 | No turn |
| Start of activities | 30/09/2019 |
|---|---|
| End of activities | 18/01/2020 |
| Show course schedule | 2019/20 Reg.2019 course timetable |
Examination board
Examination board not defined
| 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) |
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