Gravitational waves from extreme mass ratio inspirals: challenges in mapping the spacetime of massive, compact objects

In its final year of inspiral, a stellar mass (1-10 M-circle dot) body orbi ts a massive (10(5)-10(7) M-circle dot) compact object about 10(5) times, s piralling from several Schwarzschild radii to the last stable orbit. These orbits are deep in the massive object's strong field, so the gravitational waves that they produce probe the strong-field nature of the object's space time. Measuring these waves can, in principle, be used to 'map' this spacet ime, allowing observers to test whether the object is a black hole or somet hing more exotic. Such measurements will require a good theoretical underst anding of wave generation during inspiral. In this paper, I discuss the maj or theoretical challenges standing in the way of building such maps from gr avitational-wave observations, as well as recent progress in producing extr eme mass ratio inspirals and waveforms.