Exact static solutions in four dimensional Einstein-Maxwell-Dilaton gravity

Classes of exact static solutions in four-dimensional Einstein-MaxwellDilaton gravity are found. Besides of the well-known solutions previously found in the literature, new solutions are presented.It’s shown that spherically symmetric solutions, except the case of charged dilaton black hole, represent globally naked strong curvature singularities. The scalar field is believed to play an important role in physics. Nearly all generalized theories of gravity as Brans-Dicke models and Kaluza-Klein theory involve a scalar field. On the other hand the scalar field arises from low energy limit of string theory. In recent years a lot of attention has been turned to low dimensional string theory inspirited models. It turns out to be useful to study such models as a first step in the surch of the exact string theory. On the one hand the studying of low dimensional models may throw light on higher dimensional case and give some insight into the nonperturbative structure of string theory.On the other hand it leads to better understanding of some problems in pure general relativity as example black holes and the question of the scalar hair. The charged black holes solutions supporting scalar hair in the four dimensional Einstein-Maxwell-Dilaton gravity were found and studied in [1] (see also [2]). The purpose of the present article is to present classes of exact static solutions in the four dimensional Einstein-Maxwell-Dilaton gravity containing new solutions besides of the known, previously found in the literature. We consider four dimensional Einstein-Maxwell-Dilaton gravity with an action S = 1 16π ∫ dx √ −g ( R− 2g∂aφ∂bφ− eFabF ab ) (1) ∗E-mail: [email protected]