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

TL;DR

This paper introduces a $Z_2$ duality in (2+1)-dimensional Einstein-Maxwell-Dilaton gravity theories, enabling the generation of magnetically charged solutions from electric ones and exploring their relation to string theory symmetries.

Contribution

It establishes an analog of electric-magnetic duality in (2+1)D gravity theories, connecting magnetic and electric solutions and relating to string theory dualities.

Findings

Derived exact magnetically charged solutions from electric solutions.

Linked the $Z_2$ transformation to $O(2,Z)$ symmetry and $T$-duality.

Explored the duality within theories connecting BTZ gravity and string effective theory.

Abstract

We find an analog 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, 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.