Solutions of the Regge Equations on some Triangulations of CP^2

Details Solutions of the Regge Equations on some Triangulations of CP^2 Solutions of the Regge Equations on some Triangulations of CP^2

1996-06-04

arxiv.org/abs/gr-qc/9606005v2

J.Math.Phys. 38 (1997) 2577-2586

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, uuencoded revtex w/ embedded ps figure. Replaces a submission which had corrupted ps file

Scientific paper

10.1063/1.531958

Simplicial geometries are collections of simplices making up a manifold together with an assignment of lengths to the edges that define a metric on that manifold. The simplicial analogs of the Einstein equations are the Regge equations. Solutions to these equations define the semiclassical approximation to simplicial approximations to a sum-over-geometries in quantum gravity. In this paper, we consider solutions to the Regge equations with cosmological constant that give Euclidean metrics of high symmetry on a family of triangulations of CP^2 presented by Banchoff and Kuhnel. This family is characterized by a parameter p. The number of vertices grows larger with increasing p. We exhibit a solution of the Regge equations for p=2 but find no solutions for p=3. This example shows that merely increasing the number of vertices does not ensure a steady approach to a continuum geometry in the Regge calculus.

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