Dynamical damping terms for symmetry-seeking shift conditions

TL;DR

This paper introduces a new dynamical damping term for shift conditions in numerical relativity, eliminating the need for parameter tuning and improving stability in simulations of unequal-mass binary black holes.

Contribution

A novel gauge condition with a dynamical damping constant that adapts to binary parameters, enhancing stability and reducing tuning requirements in black-hole binary simulations.

Findings

Removes need for parameter tuning in shift conditions.

Provides stable evolution without instabilities.

Reduces coordinate size variations of black hole horizons.

Abstract

Suitable gauge conditions are fundamental for stable and accurate numerical-relativity simulations of inspiralling compact binaries. A number of well-studied conditions have been developed over the last decade for both the lapse and the shift and these have been successfully used both in vacuum and non-vacuum spacetimes when simulating binaries with comparable masses. At the same time, recent evidence has emerged that the standard "Gamma-driver" shift condition requires a careful and non-trivial tuning of its parameters to ensure long-term stable evolutions of unequal-mass binaries. We present a novel gauge condition in which the damping constant is promoted to be a dynamical variable and the solution of an evolution equation. We show that this choice removes the need for special tuning and provides a shift damping term which is free of instabilities in our simulations and dynamically adapts to the individual positions and masses of the binary black-hole system. Our gauge condition also reduces the variations in the coordinate size of the apparent horizon of the larger black hole and could therefore be useful when simulating binaries with very small mass ratios.