Weyl conform tensor for stationary gravitational fields

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Abstract
Our formulas for the Weyl conform tensor components generalize results published earlier by Z. Perjés for vacuum fields. We also offer an abstract version of these equations which may shed some light upon their structure. The expressions for the Weyl conform tensor are specialized to the case of small perturbations from a stationary axially symmetric background geometry. The resulting formulas supplement the expressions which Chandrasekhar and Friedman have developed for the components of the Ricci tensor. We anticipate that this will facilitate the comparison of the CF perturbation theory with the recent studies of perturbations of the Kerr metric by Press, Teukolsky, and Wald. In this connection we identify in terms of the CF field variables the fields which are involved in Teukolsky's separable field equations.