Chin. Phys., 2006, Vol. 15(1): 66-76    DOI: 10.1088/1009-1963/15/1/011
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# New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields

Gao Ya-Jun
Department of Physics, Bohai University, Jinzhou 121000,China
Abstract  The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein--Maxwell theory with $p$ Abelian gauge fields (EM-$p$ theory, for short). Two EHC structural Riemann--Hilbert (RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-$p$ theory. This symmetry group is verified to have the structure of semidirect product of Kac--Moody group $\widehat{SU(p+1,1)}$ and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme. This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.
Keywords:  extended hyperbolic complex function method      general relativity      symmetry group
Received:  16 May 2005      Revised:  04 July 2005      Published:  20 January 2006
 PACS: 02.20.-a (Group theory) 02.10.Ud (Linear algebra)
Fund: Project supported by the Science Foundation from Education Department of Liaoning Province, China (Grant No 202142036) and the National Natural Science Foundation of China (Grant No 10475036).