T-Duality and Spinning Solutions in 2 + 1 Gravity

TL;DR

This paper explores T-duality in 2+1 gravity with electromagnetic and dilaton fields, deriving a sigma-model and generating new spinning solutions across various gravity theories using the SL(2,R) duality group.

Contribution

It derives the sigma-model for 2+1 Einstein--Maxwell--Dilaton gravity and demonstrates the application of T-duality to generate new spinning solutions in multiple gravity theories.

Findings

The T-duality group is SL(2,R) for general coupling parameters.

New spinning solutions are obtained in Einstein--Maxwell, Brans--Dicke, and Einstein--Maxwell--Dilaton theories.

The duality corresponds to linear coordinate transformations along Killing orbits.

Abstract

Starting with the 2+1 Einstein--Maxwell--Dilaton system with a cosmological constant and assuming two commuting Killing symmetries we derive the corresponding $1+0 \sigma$--model. It is shown that, for general values of the coupling parameters, the $T$--duality group is $SL(2,R)$, which coincides with the group of linear coordinate transformations along the Killing orbits. This duality, along with a suitable parameter choice, is applied to obtain some new spinning solutions in the alternative gravity theories: Einstein--Maxwell, Brans--Dicke and Einstein--Maxwell--Dilaton.