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.
Received: 13 June 2003
Revised: 24 September 2003
Accepted manuscript online:
PACS:
04.40.Nr
(Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields)
Fund: Project supported by the Science Foundation from the Education Department of Liaoning Province of China (Grant No 202142036).
Cite this article:
Gao Ya-Jun (高亚军) New infinite-dimensional hidden symmetries for the stationary axisymmetric Einstein－Maxwell equations with multiple Abelian gauge fields 2004 Chinese Physics 13 602
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