Related papers: Regge Calculus as a Fourth Order Method in Numeric…
We show how to construct space time lattices with a Regge action proportional to the energy of a given Ising or Potts model macrostate. This allows to take advantage of the existence of exact solutions for these models to calculate the…
Two lattice based methods for numerical relativity, the Regge Calculus and the Smooth Lattice Relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard…
This is an informal review of the formulation of canonical general relativity and of its implications for quantum gravity; the various versions are compared, both in the continuum and in a discretized approximation suggested by Regge…
(3+1) (continuous time) Regge calculus is reduced to Hamiltonian form. The constraints are classified, classical and quantum consequences are discussed. As basic variables connection matrices and antisymmetric area tensors are used…
Regge calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The discrete Regge model…
A first order form of Regge calculus is defined in the spirit of Palatini's action for general relativity. The extra independent variables are the interior dihedral angles of a simplex, with conjugate variables the areas of the triangles.…
We propose a version of the 2D Regge calculus, in which the areas of all triangles are equal to each other. In this discretization Lund - Regge measure over link lengths is simplified considerably. Contrary to the usual Regge models with…
Simplicial approximation and the ideas associated with the Regge calculus.provide a concrete way of implementing a sum over histories formulation ofquantum gravity. A four-dimensional simplicial geometry is made up of flat four-simplices…
Using the notion of a general conical defect, the Regge Calculus is generalized by allowing for dislocations on the simplicial lattice in addition to the usual disclinations. Since disclinations and dislocations correspond to curvature and…
We consider simplest piecewise flat manifold consisting of two identical 4-tetrahedra (call it bisimplex). General relativity action for arbitrary piecewise flat manifold can be expressed in terms of sum of the (half of) bisimplex actions.…
The inclusion of source terms in discrete gravity is a long-standing problem. Providing a consistent coupling of source to the lattice in Regge Calculus (RC) yields a robust unstructured spacetime mesh applicable to both numerical…
We re-examine the approach to four-dimensional Euclidean quantum gravity based on the Regge calculus. A cut-off on the link lengths is introduced and consequently the gravitational coupling and the cosmological constant become independent…
We introduce a modified Regge calculus for general relativity on a triangulated four dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These variables satisfy constraints which are…
In the context of the teleparallel equivalent of general relativity, the Weitzenbock manifold is considered as the limit of a suitable sequence of discrete lattices composed of an increasing number of smaller an smaller simplices, where the…
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.…
With the theory of general relativity, Einstein abolished the interpretation of gravitation as a force and associated it to the curvature of spacetime. Tensorial calculus and differential geometry are the mathematical resources necessary to…
We revisit the Regge calculus model of the Kasner cosmology first considered by S. Lewis. One of the most highly symmetric applications of lattice gravity in the literature, Lewis' discrete model closely matched the degrees of freedom of…
We consider a Schwarzschild type solution in the discrete Regge calculus formulation of general relativity quantized within the path integral approach. Earlier, we found a mechanism of a loose fixation of the background scale of Regge…
In Regge calculus the space-time manifold is approximated by certain abstract simplicial complex, called a pseudo-manifold, and the metric is approximated by an assignment of a length to each 1-simplex. In this paper for each pseudomanifold…
We consider two versions of quantum Regge calculus. The Standard Regge Calculus where the quadratic link lengths of the simplicial manifold vary continuously and the Z_2-Regge Model where they are restricted to two possible values. The goal…