A Stationary Approximation to the Spacetime of a Compact Object Binary

TL;DR

This paper introduces a method to approximate the spacetime of a compact binary system in strong gravitational fields by numerically solving for a stationary spacetime that models slow orbital decay, bridging the gap between weak-field and fully dynamical approaches.

Contribution

It proposes a novel stationary approximation scheme for modeling the spacetime of inspiraling compact binaries in regimes where traditional weak-field methods fail.

Findings

Numerical results from scalar field theory support the effectiveness of the stationary approximation.

The approach maintains equilibrium by balancing incoming and outgoing radiation.

The method provides a new tool for studying strong-field binary inspirals.

Abstract

The gravitational-radiation-induced inspiral of a binary system of compact objects is considered. A scheme is described to model the regime in which the gravitational interaction is too strong to use weak-field approximation methods, but the time scale for decay of the orbits is still long compared to the orbital period, by numerically solving for a stationary spacetime which approximates the slowly evolving one. Equilibrium is to be maintained in the radiating system by imposing a balance of incoming and outgoing radiation at large distances. Numerical results from non-linear scalar field theory have shown that such an approach can be effective modelling a slowly evolving solution to a wave equation.