English

A new class of non-aligned Einstein-Maxwell solutions with a geodesic, shearfree and non-expanding multiple Debever-Penrose vector

General Relativity and Quantum Cosmology 2018-12-05 v2

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 Λ=0\Lambda=0 such solutions do exist and can be classified, after fixing the null-tetrad such that Ψ0=Ψ1=Φ1=0\Psi_0 = \Psi_1 = \Phi_1 = 0 and Φ0=1\Phi_0 = 1, according to whether the Newman-Penrose coefficient π\pi is 0 or not. The family π=0\pi = 0 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 π=0\pi = 0 both null-rays k and l are non-twisting: while it is certainly true that μ(ρ)=0\mu \Im (\rho) = 0, the case μ=0\mu = 0 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