Undergraduate Thesis Or Project
 

A Generalized Scheme for Creating Regge Calculus Models of General Relativity

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https://ir.library.oregonstate.edu/concern/undergraduate_thesis_or_projects/2801pq43b

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  • Solutions to Einstein's equations are usually found by considering ideal, simplified models. However, if the real world always matched ideal physics models, then farmers would milk black and white spheres. To combat this, Regge calculus was developed as a numerical approximation scheme for general relativity. In Regge calculus curved manifolds are approximated by a lattice of triangles where spacetime is flat on each individual triangle. Regge intended this scheme to be used for all metrics. As such, a consistent framework must exist for discretizing a manifold without relying on any prior knowledge of the metric or symmetries. The papers which discuss this are often very hard to follow or highly specialized to one specific metric without much general applicability. In this paper, the outlines of such a method of Regge calculus were found. This was done by issuing a few simple constraints on the edge lengths of the lattice. Using these constraints, equations were then derived for the angle deficits, Regge action, and metric coefficients in terms of only the edge lengths.
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