中国物理B ›› 2004, Vol. 13 ›› Issue (5): 602-611.doi: 10.1088/1009-1963/13/5/008
高亚军
Gao Ya-Jun (高亚军)
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.
中图分类号: (Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields)