  We intend to develop part of the theoretical tools needed for the detection
of gravitational waves coming from the capture of a compact object, 1-100 solar
masses, by a Supermassive Black Hole, up to a 10 billion solar masses, located
at the centre of most galaxies. The analysis of the accretion activity unveils
the star population around the galactic nuclei, and tests the physics of black
holes and general relativity. The captured small mass is considered a probe of
the gravitational field of the massive body, allowing a precise measurement of
the particle motion up to the final absorption. The knowledge of the
gravitational signal, strongly affected by the self-force - the orbital
displacement due to the captured mass and the emitted radiation - is imperative
for a successful detection. The results include a strategy for wave equations
with a singular source term for all type of orbits. We are now tackling the
evolution problem, first for radial fall in Regge- Wheeler gauge, and later for
generic orbits in the harmonic or de Donder gauge for Schwarzschild-Droste
black holes. In the Extreme Mass Ratio Inspiral, the determination of the
orbital evolution demands that the motion of the small mass be continuously
corrected by the self-force, i.e. the self-consistent evolution. At each of the
integration steps, the self-force must be computed over an adequate number of
modes; further, a differential-integral system of general relativistic
equations is to be solved and the outputs regularised for suppressing
divergences. Finally, for the provision of the computational power,
parallelisation is under examination.
