
Course unit
GENERAL RELATIVITY
SCP7081661, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
Mutuated
Course unit code 
Course unit name 
Teacher in charge 
Degree course code 
SCP7081661 
GENERAL RELATIVITY 
MARCO PELOSO 
SC2443 
ECTS: details
Type 
ScientificDisciplinary 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 
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. Fourvectors and special relativistic kinematics. Special relativistic dynamics and the energymomentum 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 blackholes. EddingtonFinkelstein, and KruskalSzekeres coordinates, Kruskal and Penrose diagrams.
8. Rotations and Kerr Geometry
Geodetic precession around a nonrotating, 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), .


