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TUW-03-18



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


D. Grumiller% latex2html id marker 2093 \setcounter{footnote}{1}\fnsymbol{footnote}, W. Kummer% latex2html id marker 2094 \setcounter{footnote}{2}\fnsymbol{footnote}







% latex2html id marker 2095 \setcounter{footnote}{1}\fnsymbol{footnote}% latex2html id marker 2096 \setcounter{footnote}{2}\fnsymbol{footnote}Institut für Theoretische Physik, Technische Universität Wien
Wiedner Hauptstr. 8-10, A-1040 Wien, Austria










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.



Daniel Grumiller 2003-08-22