The Classical Solutions of the Dimensionally Reduced Gravitational Chern-Simons Theory

TL;DR

This paper derives and analyzes all classical solutions of a dimensionally reduced 3D gravitational Chern-Simons theory, revealing its structure as a Poisson-sigma model with conserved quantities and discussing global properties.

Contribution

It provides a complete classification of classical solutions for the reduced theory using first order gravity methods, including special cases matching previous results.

Findings

All classical solutions are constructed explicitly.

The solutions are characterized by conserved charge and energy.

Global structure and special cases are discussed.

Abstract

The Kaluza-Klein reduction of the 3d gravitational Chern-Simons term to a 2d theory is equivalent to a Poisson-sigma model with fourdimensional target space and degenerate Poisson tensor of rank 2. Thus two constants of motion (Casimir functions) exist, namely charge and energy. The application of well-known methods developed in the framework of first order gravity allows to construct all classical solutions straightforwardly and to discuss their global structure. For a certain fine tuning of the values of the constants of motion the solutions of hep-th/0305117 are reproduced. Possible generalizations are pointed out.