solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看1116次
Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: Nonspherical Schwarzschild waves and singularities at null infinity. (arXiv:1709.
来源于:arXiv
We extend earlier numerical and analytical considerations of the conformally
invariant wave equation on a Schwarzschild background from the case of
spherically symmetric solutions, discussed in Class. Quantum Grav. 34, 045005
(2017), to the case of general, nonsymmetric solutions. A key element of our
approach is the modern standard representation of spacelike infinity as a
cylinder. With a decomposition into spherical harmonics, we reduce the
four-dimensional wave equation to a family of two-dimensional equations. These
equations can be used to study the behaviour at the cylinder, where the
solutions turn out to have logarithmic singularities at infinitely many orders.
We derive regularity conditions that may be imposed on the initial data, in
order to avoid the first singular terms. We then demonstrate that the fully
pseudospectral time evolution scheme can be applied to this problem leading to
a highly accurate numerical reconstruction of the nonsymmetric solutions. We
are particula 查看全文>>