Turduckening black holes: an analytical and computational study

TL;DR

This paper analyzes the turduckening technique for black hole simulations, combining analytical constraint propagation studies with 3D numerical experiments to evaluate its effectiveness and impact on gravitational wave extraction.

Contribution

It provides a rigorous analytical framework for understanding constraint violations in turduckening and compares its performance with puncture methods through detailed simulations.

Findings

Constraint violations can propagate outside black holes depending on conditions.

Turduckening produces gravitational wave signals similar to puncture methods.

Differences in waveforms decrease with larger detector distances.

Abstract

We provide a detailed analysis of several aspects of the turduckening technique for evolving black holes. At the analytical level we study the constraint propagation for a general family of BSSN-type formulation of Einstein's field equations and identify under what conditions the turducken procedure is rigorously justified and under what conditions constraint violations will propagate to the outside of the black holes. We present high-resolution spherically symmetric studies which verify our analytical predictions. Then we present three dimensional simulations of single distorted black holes using different variations of the turduckening method and also the puncture method. We study the effect that these different methods have on the coordinate conditions, constraint violations, and extracted gravitational waves. We find that the waves agree up to small but non-vanishing differences, caused by escaping superluminal gauge modes. These differences become smaller with increasing detector location.