The butterfly effect in the extreme-mass ratio inspiral problem
  Measurements of gravitational waves from the inspiral of a stellar-mass
compact object into a massive black hole are unique probes to test General
Relativity (GR) and MBH properties, as well as the stellar distribution about
these holes in galactic nuclei. Current data analysis techniques can provide us
with parameter estimation with very narrow errors. However, an EMRI is not a
two-body problem, since other stellar bodies orbiting nearby will influence the
capture orbit. Any deviation from the isolated inspiral will induce a small,
though observable deviation from the idealised waveform which could be
misinterpreted as a failure of GR. Based on conservative analysis of mass
segregation in a Milky Way like nucleus, we estimate that the possibility that
another star has a semi-major axis comparable to that of the EMRI is
non-negligible, although probably very small. This star introduces an
observable perturbation in the orbit in the case in which we consider only loss
of energy via gravitational radiation. When considering the two first-order
non-dissipative post-Newtonian contributions (the periapsis shift of the
orbit), the evolution of the orbital elements of the EMRI turns out to be
chaotic in nature. The implications of this study are twofold. From the one
side, the application to testing GR and measuring MBHs parameters with the
detection of EMRIs in galactic nuclei with a millihertz mission will be even
more challenging than believed. From the other side, this behaviour could in
principle be used as a signature of mass segregation in galactic nuclei.
