Abstract

Extreme-Mass-Ratio Inspirals (EMRIs) are astrophysical systems which are composed of a massive black hole (order 10E6 Msun) and a compact star CS (order 5Msun). Due to the nature of the system, the compact star (CS) can complete many orbits deep inside the massive black hole (MBH) potential whilst radiating GWs that carry imprinted the structure of the MBH spacetime. Therefore, EMRI detection offers a unique way to obtain direct information about the strong field near the MBH horizon. However, for EMRI detection, its orbit needs to be modelled very accurately, which in practice means solving the two body problem in General Relativity. To accurately model the CS motion, we rely on perturbation theory, where the inspiral is driven by the action of a local self-force. The computation of the self-force is still an open problem due to its mathematical and technical complexity. Moreover, along its evolution an EMRI might encounter resonant orbits, adding further difficulty to the modelling. In this talk I will review these two problems in EMRI modelling and the research that we are developing to address them.