Gravitational self-force with hyperboloidal slicing and spectral methods

TL;DR

This paper introduces a new computational framework using hyperboloidal slicing and spectral methods to accurately calculate the gravitational self-force in the Lorenz gauge, improving efficiency and extending previous scalar-field models to gravitational perturbations.

Contribution

The paper extends hyperboloidal spectral methods from scalar models to gravitational perturbations in the Lorenz gauge, enabling efficient and accurate GSF calculations.

Findings

Successfully computed Lorenz gauge metric perturbations from Regge-Wheeler gauge.

Framework allows calculation of physical quantities like radiative fluxes and redshift.

Establishes a foundation for future second-order GSF computations.

Abstract

We present a novel approach for calculating the gravitational self-force (GSF) in the Lorenz gauge, employing hyperboloidal slicing and spectral methods. Our method builds on the previous work that applied hyperboloidal surfaces and spectral approaches to scalar-field toy model [Phys. Rev. D 105, 104033 (2022)], extending them to handle gravitational perturbations. Focusing on first-order metric perturbations, we address the construction of the hyperboloidal foliation, detailing the minimal gauge choice. The Lorenz gauge is adopted to facilitate well-understood regularisation procedures, which are essential for obtaining physically meaningful GSF results. We calculate of the Lorenz gauge metric perturbation via a (known) gauge transformation from the Regge-Wheeler gauge. Our approach yields a robust framework for obtaining the metric perturbation components needed to calculate key physical quantities, such as radiative fluxes, the Detweiler redshift, and self-force corrections. Furthermore, the compactified hyperboloidal approach allows us to efficiently calculate the metric perturbation throughout the entire spacetime. This work thus establishes a foundational methodology for future second-order GSF calculations within this gauge, offering computational efficiencies through spectral methods.