Vistas in numerical relativity

TL;DR

This paper discusses the role of numerical relativity in gravitational wave detection, emphasizing the importance of well-posed formulations and gauge choices for accurate waveform modeling in Einstein's equations.

Contribution

It explores gauge choices and dynamical conditions that enable solving all Einstein equations for vacuum spacetimes, advancing numerical relativity methods.

Findings

Successfully applied to polarized Gowdy wave

Enables solving all ten vacuum Einstein equations

Highlights ongoing challenges in evolving Schwarzschild metrics

Abstract

Upcoming gravitational wave-experiments promise a window for discovering new physics in astronomy. Detection sensitivity of the broadband laser interferometric detectors LIGO/VIRGO may be enhanced by matched filtering with accurate wave-form templates. Where analytic methods break down, we have to resort to numerical relativity, often in Hamiltonian or various hyperbolic formulations. Well-posed numerical relativity requires consistency with the elliptic constraints of energy and momentum conservation. We explore this using a choice of gauge in the future and a dynamical gauge in the past. Applied to a polarized Gowdy wave, this enables solving {\em all} ten vacuum Einstein equations. Evolution of the Schwarzschild metric in 3+1 and, more generally, sufficient conditions for well-posed numerical relativity continue to be open challenges.