General-relativistic implicit hydrodynamics in polar-sliced space-time

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Abstract
We derive the equations of general-relativistic spherical hydrodynamics in a Lagrangian gauge subject to the condition of polar slicing of space-time, which gives both maximum coverage of material zones and stronger singularity avoidance than either synchronous (May and White) or maximally sliced coordinates. We present a fully relativistic, polar-sliced implicit computer code (g r i p o s) for Lagrangian spherical hydrodynamics, and present the results of computations of two test problems: the approach to hydrostatic equilibrium of a near-equilibrium, initial configuration and the collapse of pressureless dust. We compare our results to the known solutions of these two tests. We also follow the collapse to a black hole of an equilibrium configuration after pressure reduction.