Cauchy-characteristic matching for a family of cylindrical vacuum solutions possessing both gravitational degrees of freedom
arXiv:gr-qc/0002057 · doi:10.1088/0264-9381/17/16/305
Abstract
This paper is part of a long term program to Cauchy-characteristic matching (CCM) codes as investigative tools in numerical relativity. The approach has two distinct features: (i) it dispenses with an outer boundary condition and replaces this with matching conditions at an interface between the Cauchy and characteristic regions, and (ii) by employing a compactified coordinate, it proves possible to generate global solutions. In this paper CCM is applied to an exact two-parameter family of cylindrically symmetric vacuum solutions possessing both gravitational degrees of freedom due to Piran, Safier and Katz. This requires a modification of the previously constructed CCM cylindrical code because, even after using Geroch decomposition to factor out the -direction, the family is not asymptotically flat. The key equations in the characteristic regime turn out to be regular singular in nature.
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