Time-domain modelling of Extreme-Mass-Ratio Inspirals for the Laser Interferometer Space Antenna

When a stellar-mass compact object is captured by a supermassive black hole located in a galactic centre, the system losses energy and angular momentum by the emission of gravitational waves. Subsequently, the stellar compact object evolves inspiraling until plunging onto the massive black hole. These EMRI systems are expected to be one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna (LISA). However, the detection of EMRI signals will require of very accurate theoretical templates taking into account the gravitational self-force, which is the responsible of the stellar-compact object inspiral. Due to its potential applicability on EMRIs, the obtention of an efficient method to compute the scalar self-force acting on a point-like particle orbiting around a massive black hole is being object of increasing interest. We present here a review of our time-domain numerical technique to compute the self-force acting on a point-like particle and we show its suitability to deal with both circular and eccentric orbits.