Hidden symmetry of the three-dimensional Einstein-Maxwell equations

Abstract

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 $SL(2,\mathbf{R})$ transformation between the Maxwell and the dilaton fields. This $SL(2,\mathbf{R})$ transformation is identified with the Geroch transformation of the four-dimensional vacuum Einstein equation in terms of the Kałuza-Klein mechanism.

5 pages

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