  The space based interferometer LISA will be capable of detecting the
gravitational waves emitted by stellar mass black holes or neutron stars slowly
inspiralling into the supermassive black holes found in the centre of most
galaxies. The gravitational wave signal from such an extreme mass ratio
inspiral (EMRI) event will provide a unique opportunity to test whether the
spacetime metric around the central black hole is well described by the Kerr
solution. In this paper a well studied model for EMRIs around Kerr black holes
is extended to a family of parametrically deformed bumpy black holes which
preserve the basic symmetries of the Kerr metric. The new EMRI model is then
used to quantify the constraints that LISA observations of EMRIs may be able to
place on the deviations, or bumps, on the Kerr metric.
