Spinor Treatment of Stationary Space-Times

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Abstract
A generalized SU(2) spinor calculus is established on the ``background space'' V3 of the stationary space‐time. The method of spin coefficients is developed in three dimensions. The stationary field equations can be put to a form which in V3 is analogous to the Newman‐Penrose equations. A V3 filling family of curves is determined by the gravitational field and is called the eigenray congruence. Stationary space‐times may be characterized by the geometric properties of eigenrays. The relation of this classification to the algebraic ones is discussed. The method of solving the equations obtainable for various classes is illustrated on the case of nonshearing geodetic eigenrays. Assuming asymptotic flatness, we obtain the Kerr metric.
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