Time Domain Simulations of EMRIs using Finite Element Methods

This is a brief report on time-domain numerical simulations of extreme-mass-ratio binaries based on finite element methods. We discuss a new technique for solving the perturbative equations describing a point-like object orbiting a non-rotating massive black hole and the prospects of using it for the evaluation of the gravitational self-force responsible of the inspiral of these binary systems. We also discuss the perspectives of transferring this technology to the more astrophysically relevant case of a central rotating massive black hole.