The periodic standing-wave approximation: post-Minkowski computation

TL;DR

This paper advances the periodic standing-wave method to the post-Minkowski approximation in general relativity, enabling more accurate modeling of black hole and binary star inspirals by computing second-order gravitational fields.

Contribution

It introduces the first post-Minkowski approximation computations using both linearized and nonlinear approaches within the standing-wave framework.

Findings

Computed the post-Minkowski approximation via linearized and nonlinear methods

Established a computational infrastructure applicable to full general relativity

Provided initial data for numerical relativity simulations

Abstract

The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling motion of black holes and binary stars. Previous work on this model has dealt with nonlinear scalar models, and with linearized general relativity. Here we present the results of the method for the post-Minkowski (PM) approximation to general relativity, the first step beyond linearized gravity. We compute the PM approximation in two ways: first, via the standard approach of computing linearized gravitational fields and constructing from them quadratic driving sources for second-order fields, and second, by solving the second-order equations as an ``exact'' nonlinear system. The results of these computations have two distinct applications: (i) The computational infrastructure for the ``exact'' PM solution will be directly applicable to full general relativity. (ii) The results will allow us to begin supplying initial data to collaborators running general relativistic evolution codes.