General Relativity and Gravitation

, Volume 5, Issue 1, pp 25–47 | Cite as

Shear-free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism

  • Robert W. Lind
Research Articles


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.


Differential Equation Differential Geometry Special Solution Null Vector Couple Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Publishing Company Limited 1974

Authors and Affiliations

  • Robert W. Lind
    • 1
  1. 1.Department of PhysicsSyracuse UniversitySyracuse

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