Abstract
Exact solutions to Einstein's field equations, which give rise to a Stäckel-separable Hamilton-Jacobi equation of the form
are considered. It is shown that there are no solutions for whichD is a function ofx orz, orx andz. The exact solutions are of Petrov typeN and are plane polarized waves without rotation. Some of the solutions are given explicitly, up to two arbitary functions. For these solutions the Hamilton-Jacobi equation is reduced to an uncoupled set of first-order ordinary differential equations.
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References
Carter, B. (1968).Phys. Rev.,174, 1559.
Carter, B. (1968).Commun. Math. Phys.,10, 280.
Rund, H. (1973).The Hamilton-Jacobi Theory in the Calculus of Variations, (Krieger, New York).
Matravers, D. (1972).Utilitas Math.,2, 55.
Havas, P. (1975).J. Math. Phys.,16, 1461.
Israel, W. (1970).Commun. Dublin Inst. Advan. Study, A, 19.
Kundt, W., and Enters, J. (1969). InGravitation, an Introduction to Current Research, ed. Witten, L. (Wiley, New York).
Pirani, F. A. E. (1965). InLectures on General Relativity Theory, Vol. 1, Brandeis Summer Inst. in Theoretical Physics, 1964 (Prentice-Hall, Englewood Cliffs, N.J.).
Woodhouse, N. M. J. (1975).Commun. Math. Phys.,44, 9.
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Matravers, D.R. A study of some exact solutions to Einstein's field equations which yield separable Hamilton-Jacobi equations. Gen Relat Gravit 7, 937–947 (1976). https://doi.org/10.1007/BF00766419
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DOI: https://doi.org/10.1007/BF00766419