Generalized harmonic formulation in spherical symmetry

In this pedagogically structured article, we describe a generalized harmonic (GH) formulation of the Einstein equations in spherical symmetry which is regular at the origin. The GH approach has attracted significant attention in numerical relativity over the past few years, especially as applied to the problem of binary inspiral and merger. A key issue when using the technique is the choice of the gauge source functions, and recent work has provided several prescriptions for gauge drivers designed to evolve these functions in a controlled way. We numerically investigate the parameter spaces of some of these drivers in the context of fully non-linear collapse of a real, massless scalar field, and determine nearly optimal parameter settings for specific situations. Surprisingly, we find that many of the drivers that perform well in 3 + 1 calculations that use Cartesian coordinates, are considerably less effective in spherical symmetry, where some of them are, in fact, unstable.