MG15 - Talk detail

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Abstract

For non-zero cosmological constant algebraically special non-aligned Einstein-Maxwell solutions cannot have a geodesic and shearfree multiple Debever-Penrose (DP) vector. When $\Lambda=0$ solutions do exist and they can be classified, after fixing the null-tetrad such that $\Psi_0=\Psi_1=\Phi_1=0$ and $\Phi_0=1$, according to whether the Newman-Penrose coefficient $\pi$ is $0$ or not. The $\pi=0$ family has been claimed to coincide with the Griffiths (1986) solutions, containing the Cahen-Spelkens, Cahen-Leroy and Szekeres sub-families. However the case where the second null vector (which is not DP) is non-diverging appears to have been erroneously dismissed in this analysis. I reduce the sub-family in which the multiple DP vector is purely twisting to an integrable system of pde's and I present the corresponding Petrov type III families of solutions.

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