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

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.

10 pages, RevTeX

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Cited by in corpus (11)

• No hair conjecture, nonabelian hierarchies and anti-de Sitter spacetime
• General analysis of self-dual solutions for the Einstein-Maxwell-Chern-Simons theory in (1+2) dimensions
• Magnetic solutions to 2+1 dimensional gravity with dilaton field
• Static and rotating electrically charged black holes in three-dimensional Brans-Dicke gravity theories
• Magnetic point sources in three dimensional Brans-Dicke gravity theories
• Entropy for Asymptotically AdS_3 Black Holes
• Features of gravity-Yang-Mills hierarchies in d-dimensions
• T-Duality and Spinning Solutions in 2 + 1 Gravity
• Electric field in 3D gravity with torsion
• Hidden symmetry of the three-dimensional Einstein-Maxwell equations
• Thermodynamics and the Joule-Thomson expansion of dilaton black holes in 2+1 dimensions