Non-linear effects in EMRI dynamics and their imprints on gravitational waves

Understand

The largest part of any gravitational-wave inspiral of a compact binary can be understood as a slow, adiabatic drift between the trajectories of a certain referential conservative system.

• In many contexts, the phase space of this conservative system is smooth and there are no "topological transitions" in the phase space, meaning that there are no sudden qualitative changes in the character of the orbital motion during the inspiral.
• However, in this chapter we discuss the cases where this assumption fails and non-linear and/or non-smooth transitions come into play.
• In integrable conservative systems under perturbation, topological transitions suddenly appear at resonances, and we sketch how to implement the passage through such regions in an inspiral model.