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Conformal C and empty spaces of Petrov type \(N\). (English) Zbl 1029.83008

From the authors’ abstract: Conformal Einstein spaces are of particular interest in General Relativity and Quantum Gravity. We present a set of necessary and sufficient conditions for a Petrov type \(N\) space-time to be conformally related to an empty space. The conditions are developed in two stages: first, we give necessary and sufficient conditions in Newman-Penrose, spinor, and tensor notation for a space to be conformal to a \(C\)-space; second, we establish the sufficiency of a set of additional tensorial conditions for a conformal \(C\)-space to be conformal to an empty space.

MSC:

83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)

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