GW emission and relativistic dynamical friction in intermediate mass ratio inspirals

We present a set of preliminary simulations of intermediate mass ratio inspirals (IMRIs) inside dark matter (DM) spikes accounting for post-Newtonian corrections the interaction between the two black holes up to the order 2.5 in $c^2$, as well as relativistic corrections to the dynamical friction (DF) force exerted by the DM distribution. We find that, incorporating relativity reduces of a factor $1\mathrm{/}2$ the inspiral time, for equivalent initial orbital parameters, with respect to the purely classical estimates. Vice versa, neglecting the DF of the spike systematically yields longer inspiral times.