Oppenheimer-Snyder collapse with maximal time slicing and isotropic coordinates

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Abstract
The exact solution for the collapse from rest of an initially homogeneous dust sphere (Oppenheimer-Snyder collapse) provides a convenient test-bed calculation for fully general-relativistic time-dependent numerical codes which evolve matter in strong gravitational fields. Such codes are usually based on the Arnowitt-Deser-Misner 3+1 formalism, for which maximal time slicing and isotropic spatial coordinates often prove to be desirable gauge choices to constrain the lapse and shift functions. To be useful as a check on these numerical schemes, the entire Oppenheimer-Snyder solution must then be expressed in this gauge. We perform the required coordinate transformations in this paper and discuss some general features of the matter profiles and spacetime geometry in this gauge.