A New Family of Exact Solutions in 2+1 Dimensional Einstein-Maxwell-Dilaton Theory

Static, rotationally symmetric solutions are investigated for the 2+1 dimensional Einstein-Maxwell-Dilaton theories. Some exact but not general solutions have been found for these theories by many authors. To find the general exact solutions with this symmetry for arbitrary dilaton couplings to Maxwell field and to a cosmological constant, we obtain the general and simple form of the field equations by introducing new variables. These equations can be interpreted as 'equations of motion' with a constraint equation in terms of the variables. It is shown that the 'equations of motion' are analytically integrable for some particular but physically important cases of dilaton couplings, for example, one of the cases of low-energy effective string action. As a result of the application of the method found in this paper, we obtain a new family of exact solutions of the 2+1 dimensional Einstein-Maxwell-Dilaton theory under the condition of ab = 1.