Abstract
The problem of finding algebraically special solutions of the vacuum Einstein-Maxwell equations is investigated using the spin coefficient formalism of Newman and Penrose. The general case, in which the degenerate null vectors are not hypersurface orthogonal, is reduced to a problem of solving five coupled differential equations that are no longer dependent on the affine parameter along the degenerate null directions.
It is shown that the most general regular, shearfree, nonradiating solution of these equations is the Kerr-Newman metric.
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Based in part on a doctoral thesis submitted to the University of Pittsburgh (1970) while the author was NASA Predoctoral Trainee. Research also supported in part by the National Science Foundation under Grant GP-19378.
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Lind, R.W. Shear-free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism. Gen Relat Gravit 5, 25–47 (1974). https://doi.org/10.1007/BF00758073
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DOI: https://doi.org/10.1007/BF00758073