Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces

TL;DR

This paper introduces a new tetrad-based evolution system for Einstein's equations on conformally compactified hyperboloidal slices, enabling accurate numerical modeling of gravitational waves at null infinity.

Contribution

It develops a symmetric hyperbolic formulation with fixed gauge conditions suitable for high-precision numerical relativity simulations.

Findings

Formulation is regular at future null infinity.

Couples hyperboloidal slices with a tetrad formalism.

Potential for improved gravitational wave modeling.

Abstract

We present a new evolution system for Einstein's field equations which is based on tetrad fields and conformally compactified hyperboloidal spatial hypersurfaces which reach future null infinity. The boost freedom in the choice of the tetrad is fixed by requiring that its timelike leg be orthogonal to the foliation, which consists of constant mean curvature slices. The rotational freedom in the tetrad is fixed by the 3D Nester gauge. With these conditions, the field equations reduce naturally to a first-order constrained symmetric hyperbolic evolution system which is coupled to elliptic equations for the gauge variables. The conformally rescaled equations are given explicitly, and their regularity at future null infinity is discussed. Our formulation is potentially useful for high accuracy numerical modeling of gravitational radiation emitted by inspiraling and merging black hole binaries and other highly relativistic isolated systems.