# GW emission and relativistic dynamical friction in intermediate mass ratio inspirals

## TL;DR

This paper presents preliminary simulations of intermediate mass ratio inspirals within dark matter spikes, incorporating relativistic effects and dynamical friction corrections, revealing significant impacts on inspiral times.

## Contribution

It introduces the first simulations including relativistic and dynamical friction corrections for IMRIs in dark matter spikes.

## Key findings

- Relativistic corrections halve the inspiral time compared to classical estimates.
- Neglecting dynamical friction results in longer inspiral times.
- Relativistic effects are crucial for accurate modeling of IMRIs in dark matter environments.

## Abstract

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 $1/2$ 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.