中国物理B ›› 2004, Vol. 13 ›› Issue (5): 602-611.doi: 10.1088/1009-1963/13/5/008

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

高亚军   

  1. Department of Physics, Bohai University, Jinzhou 121003, China
  • 收稿日期:2003-06-13 修回日期:2003-09-24 出版日期:2004-05-06 发布日期:2005-07-06
  • 基金资助:
    Project supported by the Science Foundation from the Education Department of Liaoning Province of China (Grant No 202142036).

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

Gao Ya-Jun (高亚军)   

  1. Department of Physics, Bohai University, Jinzhou 121003, China
  • Received:2003-06-13 Revised:2003-09-24 Online:2004-05-06 Published:2005-07-06
  • Supported by:
    Project supported by the Science Foundation from the Education Department of Liaoning Province of China (Grant No 202142036).

摘要: By proposing a so-called extended hyperbolic complex (EHC) function method, an Ernst-like (p+2)×(p+2) matrix EHC potential is introduced for the stationary axisymmetric (SAS) Einstein-Maxwell theory with p Abelian gauge fields (EM-p theory, for short), then the field equations of the SAS EM-p theory are written as a so-called Hauser-Ernst-like self-dual relation for the EHC matrix potential. Two Hauser-Ernst-type EHC linear systems are established, based on which some new parametrized symmetry transformations for the SAS EM-p theory are explicitly constructed. These hidden symmetries are found to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac-Moody algebra su(p+1,1)\otimes R(t,t^{-1}) and Virasoro algebra (without centre charges). All of the SAS EM-p theories for p=0,1,2,… are treated in a unified formulation, p=0 and p=1 correspond, respectively, to the vacuum gravity and the Einstein-Maxwell cases.

关键词: stationary axisymmetric Einstein-p-Maxwell theory, extended hyperbolic complex function, infinite-dim hidden symmetries

Abstract: By proposing a so-called extended hyperbolic complex (EHC) function method, an Ernst-like $(p+2)\times(p+2)$ matrix EHC potential is introduced for the stationary axisymmetric (SAS) Einstein-Maxwell theory with p Abelian gauge fields (EM-p theory, for short), then the field equations of the SAS EM-p theory are written as a so-called Hauser-Ernst-like self-dual relation for the EHC matrix potential. Two Hauser-Ernst-type EHC linear systems are established, based on which some new parametrized symmetry transformations for the SAS EM-p theory are explicitly constructed. These hidden symmetries are found to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac-Moody algebra $su(p+1,1)\otimes R(t,t^{-1})$ and Virasoro algebra (without centre charges). All of the SAS EM-p theories for p=0,1,2,… are treated in a unified formulation, p=0 and p=1 correspond, respectively, to the vacuum gravity and the Einstein-Maxwell cases.

Key words: stationary axisymmetric Einstein-p-Maxwell theory, extended hyperbolic complex function, infinite-dim hidden symmetries

中图分类号:  (Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields)

  • 04.40.Nr
11.15.Kc (Classical and semiclassical techniques) 02.20.Tw (Infinite-dimensional Lie groups) 02.20.Sv (Lie algebras of Lie groups)