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 hyper-velocity 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 hyper-velocity binary star is found to be very small.
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