Combining Cauchy and characteristic codes. III. The interface problem in axial symmetry

This paper is part of a long term program to develop combined Cauchy and characteristic codes as investigative tools in numerical relativity. In this, the third stage of the program, attention is devoted to axisymmetric systems possessing two spatial degrees of freedom. The method relies on being able to pass information backwards and forwards across an interface exterior to any central source present. Formulas are obtained which show how it is possible to relate the canonical forms of the interior Cauchy and exterior characteristic metric functions, and their derivatives, on the interface.