Stationary vacuum fields with a conformally flat three-space. II. Proof of axial symmetry
The conjecture is proved that stationary vacuum space-times having a conformally flat three-space are axially symmetric. The proof uses the Ernst potential and the complex conjugate potential as independent coordinates. Two field equations: a combination of the Einstein equations and an integrability condition are algebraic in one of the field variables. Their coefficients, computed by employing a REDUCE program, separately vanish unless axial symmetry holds. Solution of the coefficient equations yields the proof of axial symmetry. Certain special classes of metrics must be excluded from the discussion. The axial symmetry of these exceptional classes has been proved in I.
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- 1.Lukács, B., Perjés, Z., Sebestyén, Á., and Sparling, G. A. J. (1983).Gen. Rel. Grav.,15, 511.Google Scholar
- 2.Synge, J. L. (1960).Relativity: The General Theory (North-Holland, Amsterdam).Google Scholar
- 3.Lukács, B., and Perjés, Z. (1982).Phys. Lett.,88A, 267.Google Scholar
- 4.Cosgrove, C. (1979). Ph.D. thesis, University of Sidney;J. Phys.,A10, 1481 (1977);J. Phys.,A11, 2389 (1978).Google Scholar
- 5.Lewis, T. (1932).Proc. R. Soc. London Ser. A,136, 176.Google Scholar
- 6.Eisenhart, L. P. (1950).Riemannian Geometry (Princeton University Press, Princeton, New Jersey).Google Scholar
- 7.Lukács, B., Perjés, Z., Sebestyén, Á., and Valentini, A. KFKI-1982–19 preprint.Google Scholar
- 8.Hearn, A. C. (1973).REDUCE User's Manual (University of Utah, Salt Lake City).Google Scholar