Czapor, S. R.; McLenaghan, R. G.; Wünsch, V. Conformal C and empty spaces of Petrov type \(N\). (English) Zbl 1029.83008 Gen. Relativ. Gravitation 34, No. 3, 385-402 (2002). 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. Reviewer: Grosio Stanilov (Sofia) Cited in 1 Document 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.) Keywords:\(C\)-space; conformal Einstein spaces; Bach tensor; spinor Software:NP PDFBibTeX XMLCite \textit{S. R. Czapor} et al., Gen. Relativ. Gravitation 34, No. 3, 385--402 (2002; Zbl 1029.83008) Full Text: DOI References: [1] Anderson W. G. and McLenaghan, R. G. (1994). Ann [2] Brinkmann, · JFM 50.0504.01 · doi:10.1007/BF01556083 [3] Carminati, J. and McLenaghan, R. G. (1986). Ann [4] Czapor, S. R. and McLenaghan, R. G. · Zbl 0613.53033 · doi:10.1007/BF00762558 [5] Czapor, S. R., McLenaghan, R. G., and Carminati, J. · Zbl 0758.53047 · doi:10.1007/BF00759122 [6] Czapor, S. R., McLenaghan, R. G., and Sasse, F. D. (1999). Ann. [7] Gerlach, R. and Wünsch, V. (1999). Ann [8] Kozameh, C. N., Newman, E. T., and Tod, K. P. · Zbl 0564.53011 · doi:10.1007/BF00759678 [9] Kramer, D., Stephani, H., Herlt, E., and MacCallum, M. (1980). Exact Solutions of Einstein’s Field Equations (Cambridge University Press, Cambridge). · Zbl 0449.53018 [10] Listing, M. Conformal Einstein Spaces in n-Dimensions, Ann. Global Anal. Geo. (to appear). · Zbl 1089.53030 [11] McLenaghan, R. G. (1982). Ann [12] McLenaghan, R. G. and Leroy, J. (1972) · Zbl 0243.53030 · doi:10.1098/rspa.1972.0042 [13] Newman, E. T. and Penrose, R · Zbl 0108.40905 · doi:10.1063/1.1724257 [14] Penrose, R. and Rindler, W. (1986). Spinors and space-time, Vol. 2, (Cambridge University Press, Cambridge). · Zbl 0591.53002 [15] Pirani, F. A. E. (1965). in Lectures in General Relativity, Brandeis Summer Institute in Theoretical Physics A. Trautman et al. (eds.), (Prentice-Hall Englewood Cliffs, New Jersey). pp. 249–373. · Zbl 0176.55402 [16] Szekeres, P. (1963). · Zbl 0113.44805 · doi:10.1098/rspa.1963.0124 [17] Wünsch, · Zbl 0287.53014 · doi:10.1002/mana.19760730104 [18] Wünsch, V. (1987). Wiss. [19] Wünsch, · Zbl 0711.53019 · doi:10.1002/mana.19901461503 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.