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A discretization of a continuum theory with constraints or conservedquantities is called mimetic if it mirrors the conserved laws or constraints ofthe continuum theory at the discrete level. Such discretizations have beenfound useful in continuum mechanics and in electromagnetism. We have recentlyintroduced a new technique for discretizing constrained theories. The techniqueyields discretizations that are consistent, in the sense that the constraintsand evolution equations can be solved simultaneously, but it cannot beconsidered mimetic since it achieves consistency by determining the Lagrangemultipliers. In this paper we would like to show that when applied to generalrelativity linearized around a Minkowski background the technique yields adiscretization that is mimetic in the traditional sense of the word. We showthis using the traditional metric variables and also the Ashtekar newvariables, but in the latter case we restrict ourselves to the Euclidean case.We also argue that there appear to exist conceptual difficulties to theconstruction of a mimetic formulation of the full Einstein equations, andsuggest that the new discretization scheme can provide an alternative that isnevertheless close in spirit to the traditional mimetic formulations.Comment: 14 pages, Revtex, no figures, final version to appear in JM

Consistent and mimetic discretizations in general relativity