Shock-avoiding slicing conditions: tests and calibrations

TL;DR

This paper compares shock-avoiding slicing conditions with the traditional 1+log slicing in numerical relativity, finding that shock-avoiding conditions are a stable and viable alternative with similar performance.

Contribution

It provides the first broad tests and calibrations of shock-avoiding slicing conditions in various relativistic scenarios, demonstrating their practical viability.

Findings

Shock-avoiding slicing conditions perform similarly to 1+log slicing in stability and accuracy.

Shock-avoiding conditions exhibit more gauge-dynamics but avoid gauge-shocks.

Both slicing conditions are viable options for numerical relativity simulations.

Abstract

While the 1+log slicing condition has been extremely successful in numerous numerical relativity simulations, it is also known to develop "gauge-shocks" in some examples. Alternative "shock-avoiding" slicing conditions suggested by Alcubierre prevent these pathologies in those examples, but have not yet been explored and tested very broadly. In this paper we compare the performance of shock-avoiding slicing conditions with those of 1+log slicing for a number of "text-book" problems, including black holes and relativistic stars. While, in some simulations, the shock-avoiding slicing conditions feature some unusual properties and lead to more "gauge-dynamics" than the 1+log slicing condition, we find that they perform quite similarly in terms of stability and accuracy, and hence provide a very viable alternative to 1+log slicing.