  By detecting gravitational wave signals from extreme mass ratio inspiraling
sources (EMRIs) we will be given the opportunity to check our theoretical
expectations regarding the nature of supermassive bodies that inhabit the
central regions of galaxies. We have explored some qualitatively new features
that a perturbed Kerr metric induces in its geodesic orbits. Since a generic
perturbed Kerr metric does not possess all the special symmetries of a Kerr
metric, the geodesic equations in the former case are described by a slightly
nonintegrable Hamiltonian system. According to the Poincar\'{e}-Birkhoff
theorem this causes the appearance of the so-called Birkhoff chains of islands
on the corresponding surfaces of section in between the anticipated KAM curves
of the integrable Kerr case, whenever the intrinsic frequencies of the system
are at resonance. The chains of islands are characterized by finite width, i.e.
there is a finite range of initial conditions that correspond to a particular
resonance and consequently to a constant rational ratio of intrinsic
frequencies. Thus while the EMRI changes adiabatically by radiating energy and
angular momentum, by monitoring the frequencies of a signal we can look for a
transient pattern, in the form of a plateau, in the evolution of their ratio.
We have shown that such a plateau is anticipated to be apparent in a quite
large fraction of possible orbital characteristics if the central gravitating
source is not a Kerr black hole. Moreover the plateau in the ratio of
frequencies is expected to be more prominent at specific rational values that
correspond to the strongest resonances. This gives a possible observational
detection of such non-Kerr exotic objects.

General Relativity and Quantum Cosmology