The classical solutions of the dimensionally reduced gravitational Chern-Simons theory

摘要

The Kaluza-Klein reduction of the 3d gravitational Chern-Simons term to a 2d theory is equivalent to a Poisson-sigma model with 4d 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. (C) 2003 Elsevier Science (USA). All rights reserved. [References: 31]