First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
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
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
Department of reference Department of Physics and Astronomy
E-Learning website
Mandatory attendance
Language of instruction English
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

Teacher in charge MARCO PELOSO FIS/02

Course unit code Course unit name Teacher in charge Degree course code

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 of
Individual study
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)
  • James B. Hartle, Gravity: An Introduction to Einstein's General Relativity. --: Pearson Education (US), --. Cerca nel catalogo