Physics
Scientific paper
Dec 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976gregr...7..937m&link_type=abstract
General Relativity and Gravitation, Volume 7, Issue 12, pp.937-947
Physics
1
Scientific paper
Exact solutions to Einstein's field equations, which give rise to a Stäckel-separable Hamilton-Jacobi equation of the form ,y,z)left[ {X(x)left( {{partial S}/{partial x}} right)^2 - 2left( {{partial S}/{partial x}} right)left( {{partial S}/{partial t}} right) - 2left( {{partial S}/{partial y}} right)left( {{partial S}/{partial t}} right) + Z(z)left( {{partial S}/{partial z}} right)^2 - 2left( {{partial S}/{partial z}} right)left( {{partial S}/{partial t}} right) - F(x,y,z)left( {{partial S}/{partial t}} right)^2 } right] = λ 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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