Regularizing Dual-Frame Generalized Harmonic Gauge at Null Infinity

TL;DR

This paper develops a regularized formulation of generalized harmonic gauge in numerical relativity that extends simulations to null infinity by eliminating problematic logarithmic divergences through gauge choices and constraint adjustments.

Contribution

It introduces a first order symmetric hyperbolic reduction in GHG on compactified slices that systematically removes leading-order log-terms, enabling accurate simulations at null infinity.

Findings

Successfully eradicates leading log-terms in the hyperbolic reduction.

Suppresses unphysical radiation near null infinity.

Demonstrates the approach's effectiveness in toy models.

Abstract

The dual-frame formalism leads to an approach to extend numerical relativity simulations in generalized harmonic gauge (GHG) all the way to null infinity. A major setback is that without care, even simple choices of initial data give rise to logarithmically divergent terms that would result in irregular variables and equations on the compactified domain, which would in turn prevent accurate numerical approximation. It has been shown, however, that a suitable choice of gauge and constraint addition can be used to prevent their appearance. Presently we give a first order symmetric hyperbolic reduction of general relativity in GHG on compactified hyperboloidal slices that exploits this knowledge and eradicates these log-terms at leading orders. Because of their effect on the asymptotic solution space, specific formally singular terms are systematically chosen to remain. Such formally singular terms have been successfully treated numerically in toy models and result in a formulation with the desirable property that unphysical radiation content near infinity is suppressed.