Pierre Fleury is currently a post-doctoral fellow at the Instituto de Física Teórica of Madrid (Spain), specialized in relativistic cosmology and gravitational lensing. He concluded his PhD in 2015 at the Institut d'Astrophysique de Paris, and was successively a post-doctoral researcher at the University of Cape Town and at the University of Geneva.

His main research interest consists in using cosmological observations to learn about the fundamental laws of nature.

He is also actively involved in the diffusion of knowledge, through both academic teaching and public outreach. He likes acting, cooking, playing music, and watching French movies.

I Newton's physics

I.A Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

I.B Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

I.C Lagrangian mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

I.D Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

I.E Application to the Solar System . . . . . . . . . . . . . . . . . . . . . . . . 23

Epilogue: when Newtonian physics fails . . . . . . . . . . . . . . . . . . . . . . . 28

II Einstein's theory of relativity 29

II.A Space-time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

II.B Physics in four dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

II.C Differential geometry tool kit . . . . . . . . . . . . . . . . . . . . . . . . . 45

II.D Space-time tells matter how to fall . . . . . . . . . . . . . . . . . . . . . . 52

II.E Matter tells space-time how to curve . . . . . . . . . . . . . . . . . . . . . 59

Newton versus Einstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

III The general-relativistic world 69

III.AWeak gravitational fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

III.B Gravitational waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

III.C The Schwarzschild black hole . . . . . . . . . . . . . . . . . . . . . . . . . 83

References