Evolutions of Gowdy, Brill and Teukolsky initial data on a smooth lattice

Abstract

Numerical results, based on a lattice method for computational general relativity, will be presented for Cauchy evolution of initial data for the Brill, Teukolsky and polarised Gowdy space-times. The simple objective of this paper is to demonstrate that the lattice method can, at least for these space-times, match results obtained from contemporary methods. Some of the issues addressed in this paper include the handling of axisymmetric instabilities (in the Brill space-time) and an implementation of a Sommerfeld radiation condition for the Brill and Teukolsky space-times. It will be shown that the lattice method performs particularly well in regard to the passage of the waves through the outer boundary. Questions concerning multiple black-holes, mesh refinement and long term stability will not be discussed here but may form the basis of future work.

67 pages, 18 figures

References in corpus (2)

• A numerical study of the Regge Calculus and Smooth Lattice methods on a Kasner cosmology
• A Smooth Lattice construction of the Oppenheimer-Snyder spacetime

Cited by in corpus (2)

• Nonlinear Evolution of Quadratic Gravity in 3+1 Dimensions
• A polytopal discrete de Rham complex on manifolds, with application to the Maxwell equations