Abstract
The spin connection is studied for the Kerr-Schild metric. Our choice of tetrad leads to particularly simple results. The associated complex SU(2) gauge fields for many important particular cases, including the axially symmetric stationary Kerr metric, are thus presented in a unified fashion. Static spherically symmetric cases are studied in detail, including a cosmological term. A Lorentz gauge transformation is introduced for this class such that after a further (inverse Finkelstein) coordinate transformation a very simple form is obtained in the diagonal static metric. Using this, we study the passage to the Euclidean section, leading to real (anti) self-dual SU(2) gauge fields for the uncharged case. The role of the cosmological constant concerning the Pontryagin indices is elucidated. Finally a class of solutions of the zero-mass Dirac equation is studied in an appendix. The relation of such solutions possessing stringlike singularities, to similar ones in flat space, in the presence of non-Abelian monopoles and instantons is pointed out.
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