Cauchy-characteristic matching for a family of cylindrical solutions possessing both gravitational degrees of freedom

This article is part of a long-term programme to develop Cauchy-characteristic matching (CCM) codes as investigative tools in numerical relativity. The approach has two distinct features: (a) it dispenses with an outer boundary condition and replaces this with matching conditions at an interface between the Cauchy and characteristic regions, and (b) 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 z-direction, the family is not asymptotically flat. The key equations in the characteristic regime turn out to be regular singular in nature.