- Docente: Roberto Casadio
- Credits: 6
- SSD: FIS/02
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Physics (cod. 8007)
Learning outcomes
The aim of the course is to provide an introduction to the principles of (special and general) relativity and some of their main observational consequences (relativistic kinematics, cosmology, black holes).
Course contents
The course is divided into three main parts:
1) Principles and main applications of Special Relativity.
Starting from the incompatibility between the Newtonina mechanics
and Maxwell's electrodynamics, unsuccessful attempts to detect the
aether are reviewed briefly, and Einstein;s formulation of the
principles of relativity introduced. Relativity of simultaneity is
then discussed, and Lorentz transformations derived, from which the
main kinematical consequences are deduced (length contraction, time
delation, velocity addition, Doppler effect, light aberration,
etc). Four-momentum is then defined and the dynamics of collisions
studied (energy-momentum conservation). Finally, the covariant
formalism is introduced (Minkowski space-time, Lorentz tensors) in
order to write the laws of electrodynamics in a simple form. This
part ends with a brief analysis of the Lorentz group and its
representations (including spinors).
2) Elements of differential geometry. The student is introduced
with the necessary notions and tools to describe geometric spaces
independently of the reference frame. Differential manifolds are
defined as well as general tensors and tensorial operations. In
particular, the Lie and covariant derivatives are introduced. The
role of the metric tensor is studied in details, given its key role
in general relativity.
3) Introduction to General Relativity. The principles of general
relativity, of equivalence and of general covariance are
introduced. We show how geodesics determine the motion of test
particles on a given space-time, and how Einstein equations
determine the latter from the energy-momentum tensor of a source.
The three classical tests re reviewed: Mercury's perihelion
precession, light deflection and gravitational redshift. The
general formalism is applied to the two most relevant cases:
a) the space outside a compact spherical source, described by the
Schwarzschild metric. Radial geodesics are studied and the nature
of the Schwarzschild horizon uncovered, thus introducing the notion
of black hole.
b) the evolution of the universe is investigated from the
cosmological principle of homogeneity and isotropy, leading to
simple Friedman-Robertson-Walker models. The course ends with the
Hubble law.
Readings/Bibliography
Lecture notes available from Alma DL
Teaching methods
Old style lectures on blackboard
Assessment methods
Final oral examination, with short presentation of a topic of choice, and general questions about the arguments presented during the course.
Teaching tools
The course will be presented using the blackboard.
Office hours
See the website of Roberto Casadio