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Orthogonal transitivity, invertibility, and null geodesic separability in type D electrovac solutions of Einstein's field equations with cosmological constant

par Debever, Robert ;McLenaghan, Raymond R.G.
Référence Journal of mathematical physics, 22, 8, page (1711-1726)
Publication Publié, 1980

Article révisé par les pairs

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Résumé :

It is shown without explicit integration that all Petrov type D electrovac solutions with cosmological constant for an aligned, nonsingular electromagnetic field which satisfy the generalized Goldberg-Sachs theorem, admit at least a two-parameter, abelian, orthogonally transitive group of local isometrics. In the case when the group orbits are non-null the group is invertible, and a symmetric null tetrad is shown to exist in which the principle null congruences defined by the type-D Weyl tensor are indistinguishable. An explicit example is given of a solution with null group orbits which contains as a subcase a Kinnersley vacuum solution (with the same property). It is also demonstrated that the Hamilton-Jacobi equation for the null geodesics is always solvable by separation of variables in these solutions, a fact which explains the existence of a conformai Killing tensor therein, and which gives rise to a coordinate system in which the field equations may be integrated in terms of polynomial functions. © 1981 American Institute of Physics.