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On a solution of the Einstein–Maxwell equations admitting a nonsingular electromagnetic field
1.N. Tariq and B. O. J. Tupper, Tensor N. S. 28, 83 (1974).
2.N. Tariq and B. O. J. Tupper, Gen. Relativ. Gravit. 6, 777 (1975).
3.R. G. McLenaghan and N. Tariq, J. Math. Phys. 16, 2306 (1975).
4.B. O. J. Tupper, Gen. Relativ. Gravit., to appear.
5.The conventions of this paper are the same as those of Ref. 3.
6.See Ref. 3.
7.These properties were pointed out to us by Prof. R. Debever (private communication).
8.E. T. Newman and R. Penrose, J. Math. Phys. 3, 566 (1962).
9.R. Debever, Cah. Phys. 168–169, 303 (1964).
10.R. Debever, Bull. Cl. Sci. Acad. Roy. Belg. 60, 998 (1974).
11.See Ref. 8.
12.R. Debever, communication at the Conference on Differential Geometrical Methods in Mathematical Physics. Bonn, July 1975.
13.These conditions are satisfied if and only if there exists a tetrad transformation which leaves the spin coefficients κ, ρ, σ, τ, ε, α invariant.
14.We note that the metric (5.5) is invariant under the finite isometry but the nonsingular electromagnetic field gives rise to an involution since it implies that
15.If we obtain an integral of the form which is not difficult to integrate. However, since we never need anywhere the explicit forms of A or B, we do not elaborate this calculation further.
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