Conformal C and Empty Spaces of Petrov Type N |
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| Authors: | S. R. Czapor R. G. McLenaghan V. Wünsch |
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| Affiliation: | (1) Department of Mathematics and Computer Science, Laurentian University, Ramsey Lake Rd., Sudbury, Ontario, Canada, P3E 2C6;(2) Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1;(3) Mathematisches Institut, Universität Jena, Germany |
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| 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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| Keywords: | conformal structure C-space empty space Bach tensor |
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