We show that the solution published in Ref.1 is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyperbolicity, causal symmetry and causal stability. A detailed discussion about which assumptions in the singularity theorems are not fulfilled is performed, and we show explicitly tat the solution is in accordance with those theorems. A brief discussion of the results is given.

A compact formulation for general relativistic, axisymmetric perfect fluids in stationary rotation is introduced; the case of differential rotation is included. The basic variables are differential 1-forms with immediate physical relevance. As an illustration of the method, the authors give the derivation of an irrotational solution found recently. With the matching problem in mind, stationary, axially symmetric vacuum fields are considered as formal perfect fluids; it is shown that they can always be brought to a 'rigid rotation' or to an 'irrotational' form. Two discrete transformations (reminiscent of the Kramer-Neugebauer transformation) that may be useful for solution-generating purposes are introduced. A formulation of the Ernst type is given for the 'irrotational' vacuum case.

The isometry conditions for gravitational fields are given directly at the tetrad level, rather than in terms of the metric. As an illustration, an analysis of the curvature collineations and Killing fields for a twisting type-N vacuum gravitational field is made.

The Einstein equations describing gravitational fields in vacuum are written as a compact exterior system of spinor-valued forms. A second system of equations is given, such that their integrability conditions are satisfied by virtue of the Einstein equations. This suggests the possibility of integrating the field equations by means of an inversetype procedure.

A formulation for stationary axisymmetric electromagnetic fields in general relativity is derived by casting them into the form of an anisotropic fluid. Several simplifications of the formalism are carried out in order to analyze different features of the fields, such as the derivation of electromagnetic sources for the Maxwell field in the form of thin layers, construction of new solutions, and generation techniques.