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We extend earlier numerical and analytical considerations of the conformallyinvariant wave equation on a Schwarzschild background from the case ofspherically symmetric solutions, discussed in Class. Quantum Grav. 34, 045005(2017), to the case of general, nonsymmetric solutions. A key element of ourapproach is the modern standard representation of spacelike infinity as acylinder. With a decomposition into spherical harmonics, we reduce thefour-dimensional wave equation to a family of two-dimensional equations. Theseequations can be used to study the behaviour at the cylinder, where thesolutions turn out to have logarithmic singularities at infinitely many orders.We derive regularity conditions that may be imposed on the initial data, inorder to avoid the first singular terms. We then demonstrate that the fullypseudospectral time evolution scheme can be applied to this problem leading toa highly accurate numerical reconstruction of the nonsymmetric solutions. Weare particularly interested in the behaviour of the solutions at future nullinfinity, and we numerically show that the singularities spread from thecylinder to null infinity. The observed numerical behaviour is consistent withsimilar logarithmic singularities found analytically on the cylinder. Finally,we demonstrate that even solutions with singularities at low orders can beobtained with high accuracy by virtue of a coordinate transformation thatconverts functions with logarithmic singularities into smooth solutions.

classical and quantum gravity

Fully pseudospectral solution of the conformally invariant wave equation  near the cylinder at spacelike infinity. III: Nonspherical Schwarzschild  waves and singularities at null infinity