Optimizing the third-and-a-half post-Newtonian gravitational radiation-reaction force for numerical simulations

TL;DR

This paper reformulates the 3.5 post-Newtonian gravitational radiation-reaction force into a form suitable for numerical simulations, utilizing coordinate transformations and fluid dynamics equations.

Contribution

It introduces a new, simulation-ready expression for the radiation-reaction force at 3.5 post-Newtonian order, enhancing computational modeling of gravitational systems.

Findings

Derived a form of the radiation-reaction force suitable for simulations

Utilized coordinate transformations to simplify equations

Provided an expression for the radiation field affecting the reaction force

Abstract

The gravitational radiation-reaction force acting on perfect fluids at 3.5 post-Newtonian order is cast into a form which is directly applicable to numerical simulations. Extensive use is made of metric-coefficient changes induced by functional coordinate transformations, of the continuity equation, as well as of the equations of motion. We also present an expression appropriate for numerical simulations of the radiation field causing the worked out reaction force.