Course
In
the first lecture I will review the basics of the theory of
gravitational waves. Whenever possible, I will derive things from
scratch, but a previous exposure to General Relativity would be
beneficial.
In the second lecture I will review the methods to solve Einstein's
equations, either exactly or approximately, focusing on binary systems,
which are expected to be the main sources of gravitational waves for
existing and future detectors. I will then give examples of how the
detection of gravitational waves will permit testing gravity, cosmology
and astrophysics with unprecedented accuracy.

Chapters
 Lecture I : The basics of gravitationalwave theory
 The Einstein equations
 Linearized Einstein equations and gauge transformations
 Gravitational waves in linearized gravity: the TT gauge and the quadrupole formula
 General definition of gravitational waves: the geometric optics regime
 The stressenergy tensor for gravitational waves
 A detector's response to gravitational waves: geodesic deviation and Weyl scalars
 Lecture II : Gravitationalwave physics and astrophysics with current and future detectors
 A brief overview of existing and future detectors of gravitational waves and their sources
 How to solve Einstein's equations:
 Numerical relativity in a nutshell: 3+1 split of spacetime, formulations of the Einstein equations
 Analytic approximation schemes: The PostNewtonian expansion, the selfforce formalism, the effective onebody model
 Fundamental physics, astrophysics and cosmology with gravitationalwave detectors: a few examples
 Tests of gravity theories
 Tests of the nuclear equation of state
 Measurements of the Hubble constant and Dark Energy
 Tests of the nature of black holes and the nohair theorem
 Tests of scenarios for the formation and evolution of massive black holes

