Summary
It is shown that a class of 4-dimensional Lorentzian framed space-times (defined by a linear operator satisfying certain algebraic and geometric conditions) admitting a nonsingular simple electromagnetic field possesses a two parameter abelian group of affine conformal motions. Based on this, we have studied the problem of finding various types of inheriting electromagnetic field plus perfect fluid solutions. A sub-class of such spaces exists whose geometry is conformal to a physical space-time having an invertible two parameter abelian isometry group. Thus, our work is related to the Carter's theorems on Killing Horizons.
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Duggal, K.L. Some applications of globally framed structures to relativity. Annali di Matematica pura ed applicata 153, 77–90 (1988). https://doi.org/10.1007/BF01762387
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DOI: https://doi.org/10.1007/BF01762387