A B\"acklund transformation for the Ernst equation of general relativity, published earlier by this author, is used to derive a new large family of vacuum metrics with two commuting Killing vectors from the family of Weyl or Einstein-Rosen metrics. Thus, any solution of the axially symmetric Laplace or wave equation yields a solution of the Ernst equation. Asymptotically flat Weyl metrics yield new asymptotically flat metrics. The solutions are nonstationary and may exhibit solitonlike behavior.
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B. Kent Harrison (1980) studied this question.
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