Quasi-Stationary Binary Inspiral: Project Overview

TL;DR

This paper presents a project to model gravitational radiation from binary systems in a regime with non-perturbative effects, using stationary spacetime approximations and simplified Einstein equations, with initial testing on a symmetric model.

Contribution

It introduces a novel approach to approximate evolving binary systems with stationary solutions, including new techniques for simplifying Einstein equations and boundary conditions for gravitational radiation.

Findings

Development of methods for simplifying Einstein equations with symmetries

Formulation of boundary conditions for energy conservation in radiating spacetimes

Initial testing of the stationary approximation on symmetric models

Abstract

I describe the current status of a collaboration with J.D. Romano, R.H. Price, and W. Krivan to model the geometry of and gravitational radiation emitted by a binary system of compact objects in the regime where non-perturbative gravitational effects exist, but the rate of inspiral is still small relative to the orbital frequency. The method of looking for a stationary spacetime which approximates the evolving solution is initially being tested on a simpler model with an additional translational symmetry. This report consists of a general description of the method, followed by summaries of three techniques in varying stages of development: the simplification of the Einstein equations in the presence of two commuting Killing vectors which form a non-orthogonally-transitive symmetry group, the boundary conditions appropriate to the balance of ingoing and outgoing radiation needed to reconcile a stationary radiating solution with conservation of energy, and the treatment of gravitational waves far from the sources as linearized perturbations to the Levi-Civita spacetime. The poster presentation with which this paper is associated is available on line at http://www-itp.unibe.ch/~whelan/poster.ps.gz and the current status of the project is described at http://www-itp.unibe.ch/~whelan/qsbi.html