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Mathematical equation used to find exact solutions of equations in the general theory of relativity
In mathematics, the Ernst equation[1] is an integrable non-linear partial differential equation, named after the American physicist Frederick J. Ernst [Wikidata].[2]
The Ernst equation[edit]The equation reads: ℜ ( u ) ( u r r + u r / r + u z z ) = ( u r ) 2 + ( u z ) 2 . {\displaystyle \Re (u)(u_{rr}+u_{r}/r+u_{zz})=(u_{r})^{2}+(u_{z})^{2}.}
where ℜ ( u ) {\textstyle \Re (u)} is the real part of u {\textstyle u} . For its Lax pair and other features see e.g. [3][4] and references therein.
The Ernst equation is employed in order to produce exact solutions of the Einstein's equations in the general theory of relativity.
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