A few insights into the nature of classical and quantum gravity via null-strut calculus

Abstract

Null-strut calculus is a newly developed description of geometrodynamics. It provides a discrete and geometric description of the dynamic evolution or spacelike 3-geometries. Each 3-geometry is distinguished from its neighbours by the everywhere constant value on it of the trace of extrinsic curvature. Each 3-geometry is built out of a simplicial network of quasi-isosceles tetrahedra. These tetrahedra pack together so as to form a piecewise-flat three-dimensional manifold. The authors refer to such a surface as a TET surface. The interior of each tetrahedron of TET is flat Euclidean 3-space. All of the curvature intrinsic to this surface is concentrated at the edge lengths of spacelike structs.