Abstract

The class of solutions represented by Hermitian two-by-two matrices associated to time-independent metrics which correspond to a symmetry Euclidian Killing vector is derived. The elements of this class are related by means of point-dependent unitary unimodular two-by-two matrices. It is shown that these spinor fields associated to the Schwarzschild metric are solutions of the gravitational spinor equations proposed by Sachs. The properties of covariance of the formalism under the transformations of the groupSU2 are analysed.

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