Biaxial Ellipsoid in Discrete Gravity

Abstract

We study the biaxial ellipsoid manifold in the context of discrete gravity. The metric of the ellipsoid is transformed into that of a lattice, labeling the cells using integers which become coordinates in the continuous limit. The scalar curvature in the discrete gravity framework is computed using derived explicit solutions of spin connections for this setting and is shown to successfully recover the scalar curvature in the continuous case as the number of cells is increased. Likewise, the spin connections are numerically computed in the discrete framework by solving a nonlinear system of equations obtained through the torsion-free condition. They are shown to converge to the continuous spin connections as the number of cells is increased.