The approximation of Einstein's continuum theory of gravitation by a simplicial discretization of the metric space-time manifold and the gravitational action, originally due to Regge (1961). In Regge calculus, the metric tensor associated with each simplex is expressed as a function of the squared edge lengths, which are the dynamical variables of this model Regge geometry can be viewed as a special case of a continuum Riemannian manifold with a flat metric in the interior of its 4-simplices and singular curvature assignments to its two-simplices, known as the bones or hinges (Loll 1998).
References
Cheeger, J.; Müller, W.; and Schrader, R. "Lattice Gravity or Riemannian Structure on Piecewise Linear Spaces." In Unified Theories of Elementary Particles (Ed. H. P. Breitenlohner and P. Dürr). Berlin: Springer-Verlag, pp. 176-188, 1982.
Fröhlich, J. "Regge Calculus and Discretized Gravitational Functional Integrals." In Non-Perturbative Quantum Field Theory: Mathematical Aspects and Applications, Selected Papers. Singapore: World Scientific, pp. 523-545, 1992.
Hamber, H. W. "Simplicial Quantum Gravity." In Critical Phenomena, Random Systems, Gauge Theories (Les Houches Summer School, Session XLIII, 1984). Amsterdam, Netherlands: Elsevier, pp. 375-439, 1986.
Hartle, J. B. "Simplicial Minisuperspace. I. General Discussion." J. Math. Phys. 26, 804-814, 1985.
Loll, R. "Quantum Regge Calculus." Ch. 3 in Discrete Approaches to Quantum Gravity in Four Dimensions. Living Reviews in Relativity. Potsdam, Germany: Max-Planck-Gesellschaft, 1998. http://www.livingreviews.org/Articles/Volume1/1998-13loll/node20.html.
Misner, C. W.; Thorne, K. S.; and Wheeler, J. A. "Regge Calculus." Ch. 42 in Gravitation." San Francisco, CA: W. H. Freeman, pp. 1166-1179, 1973.
Perjes, Z. I. "Regge Calculus Package." http://library.wolfram.com/infocenter/MathSource/487.
Regge, T. "General Relativity without Coordinates." Nuovo Cimento A 19, 558-571, 1961.
Rocek, M. and Williams, R. "Quantum Regge Calculus." Phys. Lett. B 104, 31-37, 1981.
Sorkin, R. "Time Evolution Problem in Regge Calculus." Phys. Rev. D 12, 385-396, 1975.
Tuckey, P. A. and Williams, R. M. "Regge Calculus: a Brief Review and Bibliography." Class. Quantum Grav. 9, 1409-1422, 1992.
Wheeler, J. A. "Geometrodynamics and the Issue of the Final State." In Relativity, Groups, and Topology (Ed. C. DeWitt and B. S. DeWitt). New York: Gordon and Breach, pp. 467-500, 1964.
Williams, R. M. "Discrete Quantum Gravity: the Regge Calculus Approach." Int. J. Mod. Phys. B 6, 2097-2108, 1992.
Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, pp. 1054-1055, 2002.