Black holes surrounded by generic matter distributions: polar perturbations and energy flux

TL;DR

This paper develops a numerical method to analyze polar gravitational perturbations of black holes surrounded by various dark matter profiles, revealing complex flux behaviors that differ from axial cases, enhancing understanding of black hole environments through gravitational waves.

Contribution

It introduces a comprehensive numerical framework for polar perturbations in black hole systems with generic matter distributions, extending previous axial analyses and enabling detailed environmental effect studies.

Findings

Polar fluxes are not solely explained by gravitational redshift.

The method applies to multiple dark matter profiles, including Hernquist, NFW, and Einasto.

Polar gravitational wave fluxes show unique behaviors compared to axial fluxes.

Abstract

We develop a numerical approach to compute polar parity perturbations within fully relativistic models of black hole systems embedded in generic, spherically symmetric, anisotropic fluids. We apply this framework to study gravitational wave generation and propagation from extreme mass-ratio inspirals in the presence of several astrophysically relevant dark matter models, namely the Hernquist, Navarro-Frenk-White, and Einasto profiles. We also study dark matter spike profiles obtained from a fully relativistic calculation of the adiabatic growth of a BH within the Hernquist profile, and provide a closed-form analytic fit of these profiles. Our analysis completes prior numerical work in the axial sector, yielding a fully numerical pipeline to study black hole environmental effects. We study the dependence of the fluxes on the DM halo mass and compactness. We find that, unlike the axial case, polar fluxes are not adequately described by simple gravitational-redshift effects, thus offering an exciting avenue for the study of black hole environments with gravitational waves.