(Sort of) Testing relativity with extreme mass ratio inspirals

The inspirals of small'' ($1 - 100 M_\odot$) compact bodies through highly relativistic orbits of massive (several $\times 10^5 M_\odot -$ several $\times 10^6 M_\odot$) black holes are among the most anticipated sources for the LISA gravitational-wave antenna. The measurement of these waves is expected to map the spacetime of the larger body with high precision, allowing us to test in detail the hypothesis that black hole candidates are described by the Kerr metric of general relativity. In this article, we will briefly describe how these sources can be used to perform such a test. These proposed measurements are often described as testing relativity’‘. This description is at best somewhat glib: Because – at least to date – all work related to these measurements assumes general relativity as the theoretical framework in which these tests are performed, the measurements cannot be said to ``test relativity’’ in a fundamental way. More accurately, they test the {\it nature of massive compact bodies within general relativity}. A surprising result for such a test could point to deviations from general relativity, and would provide an experimentally motivated direction in which to pursue tests of gravity theories beyond GR.