Symmetries of the stationary Einstein - Maxwell-dilaton system

Abstract

Gravity coupled three-dimensional σ-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 α the symmetry algebra is isomorphic to the maximal solvable subalgebra of sl(3, R). For two critical values α = 0 and α = √ 3, Killing algebra enlarges to the full sl(3, R) and su(2, 1)×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-α solutions to dilaton gravity.

Symmetries for generating string cosmologies

“…(3.2) is formally identical to the target space considered by Gal'tsov, Garcia and Kechkin within the context of 5-D, Kaluza-Klein theory admitting two commuting Killing vectors [29]. Maison first showed that this target space represents the SL(3,R)/SO(3) coset corresponding to a homogeneous symmetric Riemannian space, where the group SL(3,R) acts transitively [30].…”

“…Maison first showed that this target space represents the SL(3,R)/SO(3) coset corresponding to a homogeneous symmetric Riemannian space, where the group SL(3,R) acts transitively [30]. It can be shown by employing the Gauss decomposition of the general SL(3,R) matrix that the action (2.31) may be written in the form [29] …”

“Triangular” extremal dilatonic dyons

“…1 In the first case it is the Kerr-Newman solution of the EM theory, while in the second these were derived using the three-dimensional sigma-model on symmetric space SL(3, R)/SO (2,1) corresponding to vacuum fivedimensional gravity. The EMD theories with these two particular values of the dilaton coupling exhaust the set of models reducing to three-dimensional sigma-models on coset spaces [12], so from this kind of reasoning there are no indications on any particular status of EMD theories with other a. Meanwhile, as was shown numerically by Poletti, Twamley and Wiltshire [13], the values a = 0, 1, √ 3 are just the lowest members n = 0, 1, 2 of the "triangular" sequence of dilaton couplings a n = n(n + 1)/2,…”

Horizon regularity and dilaton coupling quantization in EMD dyons

“…The third Einstein equation is related to (7)(8) via the Bianchi identity. This system of equations possess a discrete electric-magnetic duality…”

“…6,7 In the first case it is the Kerr-Newman solution of the EM theory, while in the second these were derived using the three-dimensional sigma-model on the symmetric space SL(3, R)/SO(2, 1), corresponding to vacuum five-dimensional gravity. EMD theories with these two values of the dilaton coupling exhaust the set of models reducing to three-dimensional sigma-models on coset spaces, 8 the values a = 0, √ 3 are just the two lowest members n = 1, 2 of the "triangular" sequence of dilaton couplings a n = n(n + 1)/2 ,…”