Combining Cauchy and characteristic codes. IV. The characteristic field equations 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 the third stage attention is devoted to axisymmetric systems possessing two spatial degrees of freedom. In the second of two preliminary theoretical papers, the vacuum field equations for the characteristic region are obtained and the compactified equations are regularized.