2004/04/30 by Cayetano Di Bartolo, Rodolfo Gambini, Jorge Pullin · 1 citation
Medicine · Physics and Astronomy · #Black Holes and Theoretical Physics #Neuroblastoma Research and Treatments #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.1063/1.1841483
published as J.Math.Phys. 46 (2005) 032501 · 14 pages, Revtex, no figures, final version to appear in JMP
arxiv created 2004/11/01 · openalex publication_date 2005/02/08 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
A discretization of a continuum theory with constraints or conserved quantities is called mimetic if it mirrors the conserved laws or constraints of the continuum theory at the discrete level. Such discretizations have been found useful in continuum mechanics and in electromagnetism. We have recently introduced a new technique for discretizing constrained theories. The technique yields discretizations that are consistent, in the sense that the constraints and evolution equations can be solved simultaneously, but it cannot be considered mimetic since it achieves consistency by determining the Lagrange multipliers. In this paper we would like to show that when applied to general relativity linearized around a Minkowski background the technique yields a discretization that is mimetic in the traditional sense of the word. We show this using the traditional metric variables and also the Ashtekar new variables, but in the latter case we restrict ourselves to the Euclidean case. We also argue that there appear to exist conceptual difficulties to the construction of a mimetic formulation of the full Einstein equations, and suggest that the new discretization scheme can provide an alternative that is nevertheless close in spirit to the traditional mimetic formulations.