A new class of non-aligned Einstein-Maxwell solutions with a geodesic, shearfree and non-expanding multiple Debever-Penrose vector
Abstract
In a recent study [NVdB2017] of algebraically special Einstein-Maxwell fields it was shown that, for non-zero cosmological constant, non-aligned solutions cannot have a geodesic and shearfree multiple Debever-Penrose vector k. When such solutions do exist and can be classified, after fixing the null-tetrad such that and , according to whether the Newman-Penrose coefficient is 0 or not. The family contains the Griffiths solutions (Griffiths 1986), with as sub-families the Cahen-Spelkens, Cahen-Leroy and Szekeres metrics. It was claimed in [Griffiths 1986] and repeated in [NVdB2017] that for both null-rays k and l are non-twisting: while it is certainly true that , the case appears to have been overlooked. A family of solutions is presented in which k is twisting but non-expanding.
Keywords
Cite
@article{arxiv.1806.09950,
title = {A new class of non-aligned Einstein-Maxwell solutions with a geodesic, shearfree and non-expanding multiple Debever-Penrose vector},
author = {Norbert Van den Bergh},
journal= {arXiv preprint arXiv:1806.09950},
year = {2018}
}
Comments
9 pages, 1 figure