  There is a chance that the spacetime around massive compact objects which are
expected to be black holes is not described by the Kerr metric, but by a metric
which can be considered as a perturbation of the Kerr metric. These non-Kerr
spacetimes are also known as bumpy black hole spacetimes. We expect that, if
some kind of a bumpy black hole exists, the spacetime around it should possess
some features which will make the divergence from a Kerr spacetime detectable.
One of the differences is that these non-Kerr spacetimes do not posses all the
symmetries needed to make them integrable. We discuss how we can take advantage
of this fact by examining EMRIs into the Manko-Novikov spacetime.
