Regularization of the second-order gravitational perturbations produced by a compact object

TL;DR

This paper develops well-defined solutions for second-order gravitational perturbations caused by a compact object, addressing singularities that hinder waveform modeling for gravitational wave detectors like LISA.

Contribution

It introduces a method to regularize the second-order gravitational perturbation equations, enabling accurate waveform template generation for extreme mass ratio inspirals.

Findings

Constructed physically meaningful solutions to singular perturbation equations

Facilitated accurate gravitational waveform modeling for LISA

Addressed mathematical challenges in second-order perturbation theory

Abstract

The equations for the second-order gravitational perturbations produced by a compact-object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill-defined. Here we construct well-defined and physically meaningful solutions to these equations. These solutions are important for practical calculations: the planned gravitational-wave detector LISA requires preparation of waveform templates for the potential gravitational-waves. Construction of templates with desired accuracy for extreme mass ratio binaries, in which a compact-object inspirals towards a supermassive black-hole, requires calculation of the second-order gravitational perturbations produced by the compact-object.