The periodic standing-wave approximation: computations in full general relativity

TL;DR

This paper extends the periodic standing wave method to full general relativity, enabling approximate modeling of inspiraling binary systems with strong gravitational fields through innovative computational techniques.

Contribution

It applies the previously developed method to full general relativity, advancing the modeling of binary black holes and neutron stars in strong fields.

Findings

Numerical results align with linearized and post-Minkowski computations.

The method effectively models strong-field, slowly inspiraling binaries.

Innovative computational techniques facilitated the application in full GR.

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 binary black holes and binary neutron stars. Previous work on this project has developed a method using a few multipoles of specially adapted coordinates well suited both to the radiation and the source regions. This method had previously been applied to linear and nonlinear scalar field models, to linearized gravity, and to a post-Minkowski approximation. Here we present the culmination of this approach: the application of the method in full general relativity. The fundamental equations had previously been developed and the challenge presented by this step is primarily a computational one which was approached with an innovative technique. The numerical results of these computations are compared with the corresponding results from linearized and post-Minkowksi computations.