The impact of relativistic corrections on the detectability of dark-matter spikes with gravitational waves

TL;DR

This paper investigates how relativistic effects influence the detectability of dark matter spikes around black holes through gravitational wave signals, highlighting the importance of including these corrections for accurate modeling.

Contribution

It provides the first numerical calculation of dark matter spike profiles in full general relativity and assesses the impact of relativistic corrections on gravitational wave dephasing.

Findings

Relativistic corrections increase the gravitational wave dephasing caused by dark matter spikes.

Including relativistic effects improves the mismatch between signals with and without dark matter.

Relativistic models show higher sensitivity to dark matter effects in gravitational wave observations.

Abstract

Black holes located within a dark matter cloud can create overdensity regions known as dark matter spikes. The presence of spikes modifies the gravitational-wave signals from binary systems through changes in the gravitational potential or dynamical friction effects. We assess the importance of including relativistic effects in both the dark matter distribution and the dynamical friction. As a first step we numerically calculate the particle dark matter spike distribution in full general relativity, using both Hernquist and Navarro-Frenk-White profiles in a Schwarzschild background, and we produce analytical fits to the spike profiles for a large range of scale parameters. Then we use a post-Newtonian prescription for the gravitational-wave dephasing to estimate the effect of relativistic corrections to the spike profile and to the dynamical friction. Finally we include the torques generated by dynamical friction in fast-to-generate relativistic models for circular extreme mass-ratio inspirals around a nonspinning black hole. We find that both types of relativistic corrections positively impact the detectability of dark matter effects, leading to higher dephasings and mismatches between gravitational-wave signals with and without dark matter spikes.