Axisymmetric Stationary Solutions as Harmonic Maps

Details Axisymmetric Stationary Solutions as Harmonic Maps Axisymmetric Stationary Solutions as Harmonic Maps

1994-02-26

arxiv.org/abs/gr-qc/9402044v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 TeX pages, one table,( CINVESTAV- preprint 12/93)

Scientific paper

10.1007/BF02108050

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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