4 PHYSICAL COSMOLOGY3 RELATIVISTIC COSMOLOGY3.5 Plane Symmetric Gravitational Waves

3.6 Regge Calculus Model 

A unique approach to numerical cosmology (and numerical relativity in general) is the method of Regge Calculus in which spacetime is represented as a complex of 4-dimensional, geometrically flat simplices. The principles of Einstein's theory are applied directly to the simplicial geometry to form the curvature, action and field equations, in contrast to the finite difference approach where the continuum field equations are differenced on a discrete mesh. A 3-dimensional code implementing Regge Calculus techniques was developed recently by Gentle and Miller [29] and applied to the Kasner cosmological model. They also describe a procedure to solve the constraint equations for time asymmetric initial data on two spacelike hypersurfaces constructed from tetrahedra, since full 4-dimensional regions or lattices are used. The new method is analogous to York's procedure [58] where the conformal metric, trace of the extrinsic curvature, and momentum variables are all freely specifiable.

Although additional work is needed to apply (and develop) Regge Calculus techniques to more general spacetimes, the early results of Gentle and Miller are promising. In particular, their evolutions have reproduced the continuum Kasner solution, achieved second order convergence, and sustained numerical stability.



4 PHYSICAL COSMOLOGY3 RELATIVISTIC COSMOLOGY3.5 Plane Symmetric Gravitational Waves

image Computational Cosmology: from the Early Universe to the Large Scale Structure
Peter Anninos
http://www.livingreviews.org/lrr-1998-9
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to livrev@aei-potsdam.mpg.de