Magnetically charged solutions via an analogue of electric-magnetic duality in (2+1)-dimensional gravity theories

Abstract

We find an analogue of the electric-magnetic duality, which is a Z(2) transformation between magnetic and electric sectors of the static and rotationally symmetric solutions in a class of (2+1)-dimensional Einstein-Maxwell-dilaton gravity theories. The theories in our consideration include, in particular, a one parameter class of theories continuously connecting the Banados-Teitelboim-Zanelli (BTZ) gravity and the low-energy string effective theory. When there is no U(1) charge, we have O(2) or O(1,1) symmetry, depending on a parameter that specifies each theory. Via the Z(2) transformation, we obtain exact magnetically charged solutions from the known electrically charged solutions. We explain the relationship between the Z(2) transformation and O(2,Z) symmetry, and comment on the T duality of the string theory.