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Holonomy groups and spacetimes. (English) Zbl 0957.83014

For a given (simply connected) spacetime \(M\), the holonomy group of its connection is a subgroup of the Lorentz group \(L\); the classification of the Lie subalgebras of \(L\) gives rise to a (global) classification of spacetimes.
The paper under review gives the possible classes of holonomy when \(M\) is: a vacuum, an Einstein, a conformally flat, a null Einstein-Maxwell type, a non-null Einstein-Maxwell type or a perfect fluid spacetime, respectively.
With few exceptions, examples for each class are provided.

MSC:

83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
83C22 Einstein-Maxwell equations
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