The wave equation is present in the modeling of many physical systems: vibrating strings, electromagnetism... In general relativity, the wave equation can be seen as a first approximation of Einstein's equations to describe the propagation of deformations of space-time.

In this course, we will begin by introducing the basics of Riemannian and Lorentzian geometry necessary for the formulation of the theory of general relativity. This will then be briefly introduced (students are invited to follow the course PHY568 in parallel for a more in-depth physical presentation). The second part of the course will be on the study of wave equations: in Minkowski space-time, in curved space-time, then nonlinear, in order to give an overview of the well-posed nature of Einstein's equations

**Bibliography **

-J. Lee, Riemannian manifolds, Springer

-R. Wald, General Relativity, The University of Chicago Press.

-I. Evans, Partial differential equations, AMS Course language: French or English

**Language of the**** course:** French or English

- Teaching coordinator: Huneau Cécile