Analyzing Gravitational Waves with General Relativity
  After a short review of prominent properties of gravitational waves and the
newly born gravitational astronomy, we focus on theoretical aspects. Analytic
approximation methods in general relativity have played a crucial role in the
recent discoveries of gravitational waves. They are used to build theoretical
template banks for searching and analyzing the signals in the ground-based
detectors LIGO and Virgo, and, further ahead, space-based LISA-like detectors.
In particular, the post-Newtonian approximation describes with high accuracy
the early inspiral of compact binary systems, made of black holes or neutron
stars. It mainly consists of extending the Einstein quadrupole formula by a
series of relativistic corrections up to high order. The compact objects are
modelled by point masses with spins. The practical calculations face difficult
problems of divergences, which have been solved thanks to the dimensional
regularization. In the last rotations before the merger, the finite size
effects and the internal structure of neutron stars (notably the internal
equation of state) affect the evolution of the orbit and the emission of
gravitational waves. We describe these effects within a simple Newtonian model.
