Toward relativistic inspirals into black holes surrounded by matter

TL;DR

This paper develops a relativistic framework to analyze gravitational-wave inspirals into black holes surrounded by matter, incorporating environmental effects into the Teukolsky equation for more realistic astrophysical modeling.

Contribution

It introduces a two-parameter perturbation approach and a piecewise spacetime model to include matter environments in inspiral calculations.

Findings

Matter shells cause mode mixing and boundary condition modifications.

The framework captures oscillations of the matter shell under wave perturbations.

Provides a foundation for future waveform computations in environmental settings.

Abstract

Extreme mass ratio inspirals, compact objects spiraling into massive black holes, represent key sources for future space-based gravitational-wave detectors such as LISA. The inspirals will occur within rich astrophysical environments containing gravitating matter. Motivated by this, we develop a fully relativistic framework for inspirals under the gravitational influence of matter environments. Our approach employs a two-parameter perturbation expansion in the mass ratio and an environmental parameter. This yields a modified Teukolsky equation capturing the leading cross-order. We then implement a simple pole-dipole approximation of an axisymmetric environment through a thin matter shell and restrict to non-rotating black holes. As a result, we obtain a piecewise type D spacetime. This enables the use of Teukolsky-based methods while accounting for junction physics. The presence of the matter shell leads to effectively non-separable boundary conditions for the Teukolsky scalar and introduces mode mixing between adjacent multipoles. Additionally, the shell oscillates under the wave perturbation of the inspiral, contributing to the overall flux. The framework provides novel insights into the global dynamics of gravitational radiation in tidal environments. Furthermore, it represents a complete theoretical foundation for a future computation of inspirals and waveforms in our environmental model.