Gravitational waves of extreme-mass-ratio inspirals in a rotating black hole with Dehnen dark matter halo

TL;DR

This study analyzes gravitational wave signals from extreme-mass-ratio inspirals around rotating black holes with and without dark matter halos, revealing that dark matter significantly alters waveforms.

Contribution

It introduces a method to compute EMRI waveforms in black holes with Dehnen dark matter halos, highlighting the impact of dark matter on gravitational wave signals.

Findings

Dark matter halos cause noticeable changes in GW amplitude and phase.

Mismatch between Kerr and DMBH waveforms increases with dark matter mass and black hole spin.

Waveform differences could help probe dark matter distribution around black holes.

Abstract

Extreme Mass Ratio Inspirals (EMRIs) are among the key targe sources for the space-based gravitational wave (GW) detectors. The waveforms of the EMRIs are highly sensitive to the types of the central supermassive black hole (SBH) and can serve as a novel sensitive tool to probe the background spacetime. In this work, we compute GWs radiated from EMRIs in the backgrounds of Kerr black hole and rotating black hole with Dehnen-type dark matter halo (DMBH). Following the Teukolsky prescription, we obtain the perturbed equations for curvature tensor from the Newman-Penrose (NP) equations, and for the DMBH we obtain the radial and angular equations through separation of variables. To solve the equations with numerical method we apply the Sasaki-Nakamura (SN) transformation to convert the Teykolsky-type equation into the SN equation. We study the radiation reaction of GWs by computing the energy flux and angular momentum flux at infinity and at the horizon. The orbital evolution is then derived from the total fluxes. We extract the two polarizations of GWs by solving the equation numerically. By comparing the waveforms of Kerr and DMBH, it is found that the DM halo induces noticeable changes in both the amplitude and phase of GWs. We compute the strain of GW detector with the response function and evaluate the mismatch between the waveforms of Kerr and DMBH. The results show that the mismatch increases with the mass parameter of DM halo and the spin of the SBH.