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General Relativity and Quantum Cosmology, gr-qc
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.
