A Linear-Nonlinear Formulation of Einstein Equations for the Two-Body Problem in General Relativity

TL;DR

This paper introduces a new linear-nonlinear formulation of Einstein equations to better analyze binary compact object collisions in general relativity, focusing on separating geometric variables for improved study of transitional regimes.

Contribution

It presents a novel formulation that separates Einstein equations into fixed, nonlinear, and perturbative components, aiding the analysis of complex gravitational interactions.

Findings

Potential advantages in studying binary collisions

Enhanced understanding of linear-nonlinear transition regimes

Framework for future numerical simulations

Abstract

A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of the dynamical variables into i) a fixed conformal 3-geometry, ii) a conformal factor possessing nonlinear dynamics and iii) transverse-traceless perturbations of the conformal 3-geometry.