An Efficient Time-Domain Method to Model Extreme-Mass-Ratio Inspirals

TL;DR

This paper introduces a time-domain method using a multidomain pseudospectral approach to accurately compute the self-force in extreme-mass-ratio inspirals, crucial for gravitational wave detection with LISA.

Contribution

It presents a novel, efficient time-domain technique that avoids small-scale issues by employing a multidomain framework with spectral collocation for self-force calculations.

Findings

Method accurately computes self-force for eccentric orbits.

The multidomain approach simplifies the modeling of small objects.

Spectral collocation provides high precision results.

Abstract

The gravitational-wave signals emitted by Extreme-Mass-Ratio Inspirals will be hidden in the instrumental LISA noise and the foreground noise produced by galactic binaries in the LISA band. Then, we need accurate gravitational-wave templates to extract these signals from the noise and obtain the relevant physical parameters. This means that in the modeling of these systems we have to take into account how the orbit of the stellar-mass compact object is modified by the action of its own gravitational field. This effect can be described as the action of a local force, the self-force. We present a time-domain technique to compute the self-force for geodesic eccentric orbits around a non-rotating massive black hole. To illustrate the method we have applied it to a testbed model consisting of scalar charged particle orbiting a non-dynamical black hole. A key feature of our method is that it does not introduce a small scale associated with the stellar-mass compact object. This is achieved by using a multidomain framework where the particle is located at the interface between two subdomains. In this way, we just have to evolve homogeneous wave-like equations with smooth solutions that have to be communicated across the subdomain boundaries using appropriate junction conditions. The numerical technique that we use to implement this scheme is the pseudospectral collocation method. We show the suitability of this technique for the modeling of Extreme-Mass-Ratio Inspirals and show that it can provide accurate results for the self-force.