Hidden symmetry of the three-dimensional Einstein-Maxwell equations

Details Hidden symmetry of the three-dimensional Einstein-Maxwell equations Hidden symmetry of the three-dimensional Einstein-Maxwell equations

2001-02-06

arxiv.org/abs/gr-qc/0102023v1

Phys.Rev. D63 (2001) 104019

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages

Scientific paper

10.1103/PhysRevD.63.104019

It is shown how to generate three-dimensional Einstein-Maxwell fields from known ones in the presence of a hypersurface-orthogonal non-null Killing vector field. The continuous symmetry group is isomorphic to the Heisenberg group including the Harrison-type transformation. The symmetry of the Einstein-Maxwell-dilaton system is also studied and it is shown that there is the $SL(2,{\bf R})$ transformation between the Maxwell and the dilaton fields. This $SL(2,{\bf R})$ transformation is identified with the Geroch transformation of the four-dimensional vacuum Einstein equation in terms of the Ka{\l}uza-Klein mechanism.

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