Fully relativistic three-dimensional Cauchy-characteristic matching for physical degrees of freedom

TL;DR

This paper presents a fully relativistic 3D Cauchy-characteristic matching algorithm in numerical relativity, demonstrating improved waveform accuracy and constraint satisfaction across various test scenarios without numerical instabilities.

Contribution

The authors develop and implement a novel, approximation-free 3D CCM algorithm in a numerical relativity code, enhancing waveform precision and constraint control.

Findings

No numerical instabilities observed in tests.

Effective transfer of characteristic information improves waveform accuracy.

Smaller outer boundary radius enhances constraint satisfaction.

Abstract

A fully relativistic three-dimensional Cauchy-characteristic matching (CCM) algorithm is implemented for physical degrees of freedom in a numerical relativity code SpECTRE. The method is free of approximations and can be applied to any physical system. We test the algorithm with various scenarios involving smooth data, including the propagation of Teukolsky waves within a flat background, the perturbation of a Kerr black hole with a Teukolsky wave, and the injection of a gravitational-wave pulse from the characteristic grid. Our investigations reveal no numerical instabilities in the simulations. In addition, the tests indicate that the CCM algorithm effectively directs characteristic information into the inner Cauchy system, yielding higher precision in waveforms and smaller violations of Bondi-gauge constraints, especially when the outer boundary of the Cauchy evolution is at a smaller radius.