Algebraically degenerate solutions of the Einstein and Einstein‐Maxwell equations are studied. Explicit solutions are obtained which contain two arbitrary functions of a complex variable, one function being associated with the gravitational field and the other mainly with the electromagnetic field.

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R. P. Kerr and A. Schild, Atti Del Convegno Sulla Relatwità Generate: Problemi Dell’ Energia E Onde Gravitazionali (Anniversary Volume, Fourth Centenary of Galileo’s Birth), G. Barbéra, Ed. (Firenze, 1965), p. 173;
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H. R. Strauss, Ph.D. dissertation, The University of Texas at Austin, 1969;
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6.
Throughout, complex conjugation will be denoted by a bar.
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8.
Degenerate vacuum solutions with Z = 0 have been studied by
W.
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9.
In Kerr’s paper (Ref. 1), a different choice was made for r, namely r = Re(Z−1). The present choice of r results in somewhat simpler expressions.
10.
The sign of the parameter a is opposite to that used in earlier papers (Refs. 1 and 2). The sign of a has been chosen here so that, in the asymptotically flat coordinates of Sec. 7, the z component of the angular momentum will be+am.
11.
The complex function Y is the ratio of the two components of the spinor which corresponds to the null vector e3. The special case e3 = dυ can be included by a limiting process, e.g., by starting with (1+YȲ)−1e3 and then letting Y→∞.
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E. T.
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B. Carter, report of work prior to publication, 1968.
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© 1969 The American Institute of Physics.
1969
The American Institute of Physics
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