*The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.*

**general relativity**.

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1 |
At the end of this teaching unit, the student will be able:
1. to think critically about Newton's universal gravitation; 2. to look at familiar phenomena (inertia, free fall, tides, etc.) from a different angle; 3. to understand gravitation as an apparent force that manifests itself through a space-time curvature; 4. to visualize the expansion of the universe on the basis of a Copernican principle; 5. to fully appreciate the impact (in the very long term) of fundamental research that feeds today's applied research. |

*The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.*

2. From Newton's to Einstein's mechanics.

3. Einstein's equivalence principle.

4. Some features of Riemannian geometry.

5. Einstein's equations in the vacuum.

6. Classic tests of general relativity.

7. Black holes.

8. Einstein's equations in the presence of matter.

9. The cosmological principle.

10. The Friedmann-Lemaître equations.

Consequently, we choose:

- lectures on the theory with, in parallel, many applications in physics;

- exercise sessions covering other physics applications.

The incoherence between Newton's theory of instantaneous gravity and Einstein's special relativity leads to general relativity.

Many exercises will be posed and solved with the Riemannian geometry as a background that underlies this theory.

Inductive approach, essentially based upon physical observation, and an introduction to new mathematical formalisms:

- from the displacement of Mercury's perihelion to a relativistic theory of gravitation;

- free fall of bodies in Riemann's geometry;

- recession of galaxies in the Friedmann-Lemaître dynamical models.

Written exam including a problem to solve in the context of a metric theory of gravitation.

Written exam including questions on the development of concepts in physics in connection to universal gravity (from Newton to Einstein) and their coherent mathematical formulation.

**PHYS**