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The infinitesimal holonomy group structure of space-time is discussed and related to the Petrov type of the Weyl tensor and the algebraic (Segré) type of the energy-momentum tensor. The number of covariant derivatives of the curvature tensor required to determine the infinitesimal holonomy group is determined in each case and the complete classification scheme is tabulated. Some special cases of physical interest are investigated in more detail. A geometrical approach is followed throughout.
Hall et al. (Mon,) studied this question.
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