New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields

doi:10.1088/1009-1963/15/1/011

中国物理B ›› 2006, Vol. 15 ›› Issue (1): 66-76.doi: 10.1088/1009-1963/15/1/011

New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields

高亚军

Department of Physics, Bohai University, Jinzhou 121000,China

收稿日期:2005-05-16 修回日期:2005-07-04 出版日期:2006-01-20 发布日期:2006-01-20
基金资助:
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).

New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields

Gao Ya-Jun (高亚军)

Department of Physics, Bohai University, Jinzhou 121000,China

Received:2005-05-16 Revised:2005-07-04 Online:2006-01-20 Published:2006-01-20
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: general relativity, extended hyperbolic complex function method, symmetry group

中图分类号: (Group theory)

02.20.-a

02.10.Ud (Linear algebra)

高亚军. New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields[J]. 中国物理B, 2006, 15(1): 66-76.

Gao Ya-Jun (高亚军). New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields[J]. Chinese Physics, 2006, 15(1): 66-76.

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New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields

New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields

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