I look for derivation of Ernst equation - an equation for complex function which is(adsbygoogle = window.adsbygoogle || []).push({});

equivalent to Einstein equation in case of metric with two commuting killing vectors.

I know this equation but I wonder how it may be derived. I also heard that teher is

a simple procedure which allow to construct many solution of this equation using only

one. Does anyone know how it works?

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# Ernst equation

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