New self-force method via elliptic partial differential equations for Kerr inspiral models

TL;DR

This paper introduces a novel elliptic PDE-based method to compute the Lorenz gauge self-force on a compact object in Kerr spacetime, improving numerical stability for gravitational wave modeling.

Contribution

The new elliptic PDE approach overcomes previous hyperbolic PDE instabilities, enabling more reliable self-force calculations in Kerr black hole inspiral models.

Findings

Successfully calculated scalar self-force in Kerr spacetime

Demonstrated numerical stability of the elliptic PDE method

Paved the way for future Kerr metric perturbation computations

Abstract

We present a new method designed to avoid numerical challenges that have impeded calculation of the Lorenz gauge self-force acting on a compact object inspiraling into a Kerr black hole. This type of calculation is valuable in creating waveform templates for extreme mass-ratio inspirals, which are an important source of gravitational waves for the upcoming Laser Interferometer Space Antenna mission. Prior hyperbolic partial differential equation (PDE) formulations encountered numerical instabilities involving unchecked growth in time; our new method is based on elliptic PDEs, which do not exhibit instabilities of that kind. For proof of concept, we calculate the self-force acting on a scalar charge in a circular orbit around a Kerr black hole. We anticipate this method will subsequently facilitate calculation of first-order Lorenz gauge Kerr metric perturbations and self-force, which could serve as a foundation for second-order Kerr self-force investigations.