Introduction to Regge Calculus for Gravitation

TL;DR

This paper introduces Regge Calculus as a discrete approach to modeling spacetime curvature in general relativity, providing a pedagogical overview and key results for discretizing Einstein's theory.

Contribution

It offers a pedagogical introduction to Regge Calculus and summarizes main results in discretizing Einstein's gravitation theory.

Findings

Regge Calculus uses triangulation to describe curvature discretely.

Main results include a discretized formulation of Einstein's equations.

Provides foundational understanding for numerical relativity methods.

Abstract

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 study the spacetime manifold in the context of Einstein's theory. In 1961, Tullio Regge published a work on which he uses the old idea of triangulation of surfaces aiming the description of curvature, and, therefore, gravitation, through the use of discrete calculus. In this paper, we approach Regge Calculus pedagogically, as well as the main results towards a discretized version of Einstein's theory of gravitation.