Second-order gravitational self-force

TL;DR

This paper develops a new method to derive the second-order gravitational self-force acting on compact objects in curved spacetime, crucial for improving gravitational wave templates for detectors like LISA.

Contribution

It introduces a novel derivation method for the second-order gravitational self-force and confirms its consistency with previous first-order results.

Findings

Derived a new expression for the second-order gravitational self-force.

Validated the method by reproducing the first-order self-force expression.

Facilitates the creation of more accurate gravitational wave templates.

Abstract

We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact-object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the first-order gravitational self-force. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the second-order gravitational self-force. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveforms templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational self-force will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational-waves that are emitted from extreme mass-ratio binaries.