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_⊙) body orbits a massive (10⁵-10⁷ M_⊙) compact object about 10⁵ times, spiralling 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 spacetime. Measuring these waves can, in principle, be used to `map' this spacetime, allowing observers to test whether the object is a black hole or something more exotic. Such measurements will require a good theoretical understanding of wave generation during inspiral. In this paper, I discuss the major theoretical challenges standing in the way of building such maps from gravitational-wave observations, as well as recent progress in producing extreme mass ratio inspirals and waveforms.