A brief review of Regge calculus in classical numerical relativity

We briefly review past applications of Regge calculus in classical numerical relativity, and then outline a programme for the future development of the field. We briefly describe the success of lattice gravity in constructing initial data for the head-on collision of equal mass black holes, and discuss recent results on the efficacy of Regge calculus in the continuum limit.Comment: 2 pages, submitted to the Proceedings of the IX Marcel Grossmann Meeting, Rome, July 2-8, 200

Time in Quantum Geometrodynamics

We revisit the issue of time in quantum geometrodynamics and suggest a quantization procedure on the space of true dynamic variables. This procedure separates the issue of quantization from enforcing the constraints caused by the general covariance symmetries. The resulting theory, unlike the standard approach, takes into account the states that are off shell with respect to the constraints, and thus avoids the problems of time. In this approach, quantum geometrodynamics, general covariance, and the interpretation of time emerge together as parts of the solution of the total problem of geometrodynamic evolution.Comment: 17 pages, 0 figures, formatted with LaTex, IJMP-A in pres

The Hilbert Action in Regge Calculus

The Hilbert action is derived for a simplicial geometry. I recover the usual Regge calculus action by way of a decomposition of the simplicial geometry into 4-dimensional cells defined by the simplicial (Delaunay) lattice as well as its dual (Voronoi) lattice. Within the simplicial geometry, the Riemann scalar curvature, the proper 4-volume, and hence, the Regge action is shown to be exact, in the sense that the definition of the action does not require one to introduce an averaging procedure, or a sequence of continuum metrics which were common in all previous derivations. It appears that the unity of these two dual lattice geometries is a salient feature of Regge calculus.Comment: 6 pages, Plain TeX, no figure