Modelling Extreme-Mass-Ratio Inspirals using Pseudospectral Methods

TL;DR

This paper presents a novel time-domain pseudospectral method for calculating the self-force on a scalar particle in Schwarzschild spacetime, effectively handling singularities and small scales by domain decomposition.

Contribution

The paper introduces a new pseudospectral approach that divides the domain to accurately compute self-force without resolving small length scales or facing numerical issues.

Findings

Effective domain decomposition at the particle interface

Avoidance of resolving small length scales

Mitigation of numerical problems from singular solutions

Abstract

We introduce a new time-domain method for computing the self-force acting on a scalar particle in a Schwarzschild geometry. The principal feature of our method consists in the division of the spatial domain into several subdomains and locating the particle at the interface betweem two them. In this way, we avoid the need of resolving a small length scale associated with the presence of a particle in the computational domain and, at the same time, we avoid numerical problems due to the low differentiability of solutions of equations with point-like singular behaviour.