Use of conformal, mapping to construct new solutions of the Einstein equations
- 21 Downloads
A method is obtained for constructing new solutions of the Einstein equations from known solutions, beginning with the structure of the Einstein tensor and using conformai mapping. The sollowing cases are considered: transformation of vacuum solutions into hydrodynamic solutions and the transformation of hydrodynamic solutions into solutions of the same type. A necessary and sufficient condition, imposed on the vacuum metric, is found which guarantees that solutions with a hydrodynamic energy-momentum tensor will be produced from vacuum solutions.
KeywordsEinstein Equation Vacuum Solution Einstein Tensor Hydrodynamic Solution Conformai Mapping
Unable to display preview. Download preview PDF.
- 1.I. M. Dozmorov, Izv. VUZ SSSR, Fiz., No. 9, 52 (1970).Google Scholar
- 2.I. Ehlers, Colloq. Internat. Centre Nat. Rech. Scient.,91, 275 (1962).Google Scholar
- 3.M. M. Kumar, Nuovo Cimento,63, 559 (1969).Google Scholar
- 4.J. L. Synge, Relativity: The General Theory, North Holland, Amsterdam (1960).Google Scholar
- 5.K. Yano and S. Bochner, Curvature and Betti Numbers, Princeton University Press, Princeton (1953).Google Scholar
- 6.G. I. Kruchkovich, Usp. Matem. Nauk,12, No. 6, 153 (1957).Google Scholar
- 7.G. I. Kruchkovich, “Kagan spaces,” in: V. F. Kagan, Subprojective Spaces [in Russian], Moscow (1961), p. 177.Google Scholar
- 8.P. K. Rashevskii, Proceedings of the Seminar on Vector and Tensor Analysis [in Russian], No. 1 (1933), p. 126.Google Scholar
- 9.H. L. de Vries, Math. Zeitschr., No. 3, 328 (1954).Google Scholar
- 10.A. Z. Petrov, New Methods in the General Theory of Relativity [in Russian], Moscow (1966).Google Scholar