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Axisymmetric Stationary Solutions as Harmonic Maps

Tonatiuh Matos·Jerzy Plebanski
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Abstract

We present a method for generating exact solutions of Einstein equations in vacuum using harmonic maps, when the spacetime possesses two commutating Killing vectors. This method consists in writing the axisymmetric stationry Einstein equations in vacuum as a harmonic map which belongs to the group SL(2,R), and decomposing it in its harmonic "submaps". This method provides a natural classification of the solutions in classes (Weil's class, Lewis' class etc).

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Tonatiuh Matos, Jerzy Plebanski. 1994-02-26. Axisymmetric Stationary Solutions as Harmonic Maps. https://doi.org/10.1007/bf02108050

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