2023-2024 / SPAT0260-1

Particles and gravitation


10h Th, 5h Pr

Number of credits

 Master in space sciences (120 ECTS)2 crédits 


Jean-René Cudell

Language(s) of instruction

English language

Organisation and examination

Teaching in the second semester


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

Study of field theory in curved spacetime.


1. Particle creation in an expanding universe

2. The Unruh effect

3. Discussion R1

4. The Hawking temperature 

5. The thermodynamics of black holes

6. Discussion R2

7-9. Inflation

10. Discussion R3


Learning outcomes of the learning unit

These lectures will discuss the possible relationships between some key observables in astrophysics and the present status of particle physics, mainly concerning dark matter, inflation and black holes.
At the end of the course, students will be able:

1) to understand the modern concept of particle, and its dependence on the frame of reference;
2) to calculate particle creation effects associates with gravity;
3) to calculate the entropy of a black hole.

Prerequisite knowledge and skills

SPAT0162-1 or an equivalent course should be taken before this course. Similarly, Schwarzschild, de Sitter and Rindler metrics are supposed to be known.

Planned learning activities and teaching methods

This course is based on lectures,  and to discussion sessions where problems (see the course webpages for the list) are discussed, as shown in the table of contents. The problems will be solved by the students, under the guidance of the instructor. Preparing them is strongly advised.

Mode of delivery (face to face, distance learning, hybrid learning)

The references for each lecture, notes and the list of problems are available on the course web pages.

Recommended or required readings

Viatcheslav Mukhanov and Sergei Winitzki, "Introduction to Quantum Effects in Gravity", Cambridge University Press, 2007.

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions ) AND oral exam

Additional information:

Written exam, followed by a discussion. The first question is on the theory, and the list of possible questions is available on the course web pages (it is subject to change during the year). The second question (given after the theory question is returned) is an open-book exercise. The written part lasts 2 hours.

Work placement(s)

Organisational remarks and main changes to the course

The course will be organised in 10 one-and-a-half-hour lectures/discussion sessions (see contents).


Jean-René Cudell
Institute of physics  19A Allée du 6 août Bldg B5a (4th floor, room 4/44) Université de Liège Tél. : 04/3663654
E-mail: jr.cudell@uliege.be
Web pages: http://www.theo.phys.ulg.ac.be

Association of one or more MOOCs