Symmetries of the stationary Einstein--Maxwell--dilaton theory

Details Symmetries of the stationary Einstein--Maxwell--dilaton theory Symmetries of the stationary Einstein--Maxwell--dilaton theory

1995-04-28

arxiv.org/abs/hep-th/9504155v1

Class.Quant.Grav. 12 (1995) 2887-2903

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 24 pp

Scientific paper

10.1088/0264-9381/12/12/007

Gravity coupled three--dimensional $\sigma$--model describing the stationary Einstein--Maxwell--dilaton system with general dilaton coupling is studied. Killing equations for the corresponding five--dimensional target space are integrated. It is shown that for general coupling constant $\alpha$ the symmetry algebra is isomorphic to the maximal solvable subalgebra of $sl(3,R)$. For two critical values $\alpha =0$ and $\alpha =\sqrt{3}$, Killing algebra enlarges to the full $sl(3,R)$ and $su(2,1)\times R$ algebras respectively, which correspond to five--dimensional Kaluza--Klein and four--dimensional Brans--Dicke--Maxwell theories. These two models are analyzed in terms of the unique real variables. Relation to the description in terms of complex Ernst potentials is discussed. Non--trivial discrete maps between different subspaces of the target space are found and used to generate new arbitrary--$\alpha$ solutions to dilaton gravity.

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