Geometric Computation - Null Strut Geometrodynamics and the Inchworm Algorithm
This paper introduces the development of a geometrodynamic approach to the solution of Einstein's equations. A prescription describing a specific and natural 3+1 split of spacetime into space plus time in Regge calculus is presented. Here the dynamics of geometry is described via a succession of closed, spacelike hypersurfaces of constant mean curvature, each built of quasi isosceles tetrahedrons (teted hypersurface). Any given teted hypersurface is linked via light rays or null struts to an earlier and later momentum-like structure built of quasi truncated octahedrons, thereby forming a 3-layered sandwich. Successive such 3-layered sandwiches interlock and interpenetrate forming the enveloping 4-dimensional spacetime geometry.
Dynamical Spacetimes and Numerical Relativity
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