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.
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