Numerical Calculation of Conformally Smooth Hyperboloidal Data

Abstract

This is the third paper in a series describing a numerical implementation of the conformal Einstein equation. This paper describes a scheme to calculate (three) dimensional data for the conformal field equations from a set of free functions. The actual implementation depends on the topology of the spacetime. We discuss the implementation and exemplary calculations for data leading to spacetimes with one spherical null infinity (asymptotically Minkowski) and for data leading to spacetimes with two toroidal null infinities (asymptotically A3). We also outline the (technical) modifications of the implementation needed to calculate data for spacetimes with two and more spherical null infinities (asymptotically Schwarzschild and asymptotically multiple black holes).

22 pages, 8 figures, revtex4

Cited by in corpus (6)

• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• From Now to Timelike Infinity on a Finite Grid
• Numerical relativity with the conformal field equations
• Free evolution of the hyperboloidal initial value problem in spherical symmetry
• Conformal compactification and affine-null metric formulation of the Einstein equations
• Construction of hyperboloidal initial data