Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity

Abstract

We study the scalar, conformally invariant wave equation on a four-dimensional Minkowski background in spherical symmetry, using a fully pseudospectral numerical scheme. Thereby, our main interest is in a suitable treatment of spatial infinity, which is represented as a cylinder. We consider both Cauchy problems, where we evolve data from a Cauchy surface to future null infinity, as well as characteristic initial value problems with data at past null infinity, and demonstrate that highly accurate numerical solutions can be obtained for a small number of grid points.

16 pages, 6 figures

References in corpus (2)

• The second order spin-2 system in flat space near space-like and null-infinity
• Fully pseudospectral time evolution and its application to 1+1 dimensional physical problems

Cited by in corpus (8)

• The numerical initial boundary value problem for the generalized conformal field equations
• Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. II: Schwarzschild background
• Numerical construction of initial data for Einstein's equations with static extension to space-like infinity
• Spectral methods for the spin-2 equation near the cylinder at spatial infinity
• Fully pseudospectral solution of the conformally invariant wave equation on a Kerr background
• Explorations of the infinite regions of space-time
• Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: Nonspherical Schwarzschild waves and singularities at null infinity
• The characteristic initial value problem for the conformally invariant wave equation on a Schwarzschild background