  We have developed a new method for post-Newtonian, high-precision integration
of stellar systems containing a super-massive black hole (SMBH), splitting the
forces on a particle between a dominant central force and perturbations. We
used this method to perform fully collisional N-body simulations of
inspiralling intermediate-mass black holes (IMBHs) in the centre of the Milky
Way. We considered stellar cusps of different power-law indices and analysed
the effects of IMBHs of different masses, all starting from circular orbits at
an initial distance of 0.1 pc.
  Our simulations show how IMBHs deplete the central cusp of stars, leaving
behind a flatter cusp with slope consistent with what has recently been
observed. If an additional IMBH spirals into such a flat cusp, it can take 50
Myr or longer to merge with the central SMBH, thus allowing for direct
observation in the near future. The final merger of the two black holes
involves gravitational wave radiation which may be observable with planned
gravitational wave detectors.
  Furthermore, our simulations reveal detailed properties of the hypervelocity
stars (HVSs) created, and how generations of HVSs can be used to trace IMBHs in
the Galactic Centre. We find that significant rotation of HVSs (which would be
evidence for an IMBH) can only be expected among very fast stars (v > 1000
km/s). Also, the probability of creating a hypervelocity binary star is found
to be very small.
