Gauge fixing for the simulation of black hole spacetimes

Abstract

I consider the initial-boundary-value-problem of nonlinear general relativistic vacuum spacetimes, which today cannot yet be evolved numerically in a satisfactory manner. Specifically, I look at gauge conditions, classifying them into gauge evolution conditions and gauge fixing conditions. In this terminology, a gauge fixing condition is a condition that removes all gauge degrees of freedom from a system, whereas a gauge evolution condition determines only the time evolution of the gauge condition, while the gauge condition itself remains unspecified. I find that most of today's gauge conditions are only gauge evolution conditions. I present a system of evolution equations containing a gauge fixing condition, and describe an efficient numerical implementation using constrained evolution. I examine the numerical behaviour of this system for several test problems, such as linear gravitational waves or nonlinear gauge waves. I find that the system is robustly stable and second-order convergent. I then apply it to more realistic configurations, such as Brill waves or single black holes, where the system is also stable and accurate.