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