Abstract
Held has proposed an integration procedure within the GHP formalism built around four real, functionally independent, zero-weighted scalars. He suggests that such a procedure would be particularly simple for the “optimal situation”, when the formalism directly supplies the full quota of four scalars of this type; a spacetime without any Killing vectors would be such a situation. Wils has recently obtained a conformally flat, pure radiation metric, which has been shown by Koutras to admit no Killing vectors, in general. In order to present a simple illustration of the ghp integration procedure, we obtain systematically the complete class of conformally flat, pure radiation metrics, which are not plane waves. Our result shows that the conformally flat, pure radiation metrics are a larger class than Wils has obtained.
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REFERENCES
Geroch, R., Held, A., and Penrose, R. (1973). J. Math. Phys. 14, 874.
Held, A. (1974). Commun. Math. Phys. 37, 311.
Edgar, S. B. (1980). Gen Rel. Grav. 12, 347.
Edgar, S. B. (1992). Gen Rel. Grav. 24, 1267.
Held, A. (1985). In Galaxies, Axisymmetric Systems and Relativity, M. A. H. MaCallum, ed. (Cambridge University Press, Cambridge). p.208.
Held, A. (1975). Commun. Math. Phys. 44, 211.
Held, A. (1976). Gen. Rel. Grav. 7, 177.
Held, A. (1976). J. Math. Phys. 17, 39.
Stewart, J. M., and Walker, M. (1974). Proc. Roy. Soc. Lond. A341, 49.
Newman, E. T., and Penrose, R. (1962). J. Math. Phys. 3, 566.
Newman, E. T., and Unti, T. (1962). J. Math. Phys. 3, 891.
Newman, E. T., and Unti, T. (1963). J. Math. Phys. 4, 1467.
Edgar, S. B., and Ludwig, G. (1997). Gen. Rel. Grav. 29, 19.
Kolassis, Ch. (1996). Gen. Rel. Grav. 28, 787.
Kolassis, Ch., and Griffith, J. B. (1996). Gen. Rel. Grav. 28, 805.
Ludwig, G., and Edgar, S. B. (1996). Gen. Rel. Grav. 28, 707.
Wils, P. (1989). Class. Quantum Grav. 6, 1243.
Koutras, A. (1992). Class. Quantum Grav. 9, L143.
Koutras, A. and McIntosh, C. (1996). Class. Quantum Grav. 13, L47.
Kramer, D., Stephani, H., MacCallum, M. A. H., and Herlt, E. (1980). Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge).
McLenaghan, R. G., Tariq, N., and Tupper, B. O. J. (1975). J. Math. Phys. 16, 829.
Kundt, W. (1962). Proc. Roy. Soc. Lond. A270, 328.
Edgar, S. B., and Ludwig, G. (1997). Class. Quantum Grav. 14, L65.
Skea, J. E. F. (1997). Class. Quantum Grav. 14, 2393.
Åman, J. E. (1987). Manual for CLA SSI: Classification programs for geometries in General Relativity. (Third provisional edition.) Technical Report, Institute of Theoretical Physics, University of Stockholm.
Skea, J. E. F. (1997). “Type N space-times whose invariant classifications require the fourth covariant derivative of the Riemann tensor.” To appear in Class. Quantum Grav.
Skea, J. E. F. (1997). “The On-Line Exact Solution and Invariant Classification Database.” Currently available at http://edradour.symbcomp.uerj.br and mirrors detiled in that homepage.
Karlhede, A. (1980). Gen. Rel. Grav. 12, 693.
Collins, J. M., d'Inverno, R. A. and Vickers, J. A. (1990). Class. Quantum Grav. 7, 2005.
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Edgar, S.B., Ludwig, G. Integration in the GHP Formalism III: Finding Conformally Flat Radiation Metrics as an Example of an “Optimal Situation”. General Relativity and Gravitation 29, 1309–1328 (1997). https://doi.org/10.1023/A:1018820031537
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DOI: https://doi.org/10.1023/A:1018820031537