Extreme mass ratio inspirals into black holes surrounded by matter

TL;DR

This paper develops a systematic approach to model extreme mass ratio inspirals (EMRIs) around black holes influenced by surrounding matter, incorporating complex gravitational effects and using canonical perturbation theory for efficient computation.

Contribution

It introduces a novel method to include external matter effects in EMRI modeling using perturbation theory, extending the standard black hole models.

Findings

Incorporates redshift, frame-dragging, and quadrupolar tide effects from surrounding matter.

Provides a framework for efficient computation of mildly eccentric inspirals in perturbed fields.

Demonstrates advantages of canonical perturbation theory in EMRI modeling with non-standard backgrounds.

Abstract

Inspirals of stellar-mass compact objects into massive black holes, known as extreme mass ratio inspirals (EMRIs), are one of the key targets for upcoming space-based gravitational-wave detectors. In this paper we take the first steps needed to systematically incorporate the effect of external gravitating matter on EMRIs. We model the inspiral as taking place in the field of a Schwarzschild black hole perturbed by the gravitational field of a far axisymmetric distribution of mass enclosing the system. We take into account the redshift, frame-dragging, and quadrupolar tide caused by the enclosing matter, thus incorporating all effects to inverse third order of the characteristic distance of the enclosing mass. Then, we use canonical perturbation theory to obtain the action-angle coordinates and Hamiltonian for mildly eccentric precessing test-particle orbits in this background. Finally, we use this to efficiently compute mildly eccentric inspirals in this field and document their properties. This work shows the advantages of canonical perturbation theory for the modeling EMRIs, especially in the cases when the background deviates from the standard black hole fields.