Integrable 1+1 dimensional gravity models

Details Integrable 1+1 dimensional gravity models Integrable 1+1 dimensional gravity models

1996-12-20

arxiv.org/abs/gr-qc/9612058v1

Int.J.Mod.Phys.A12:13-22,1997

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, Latex; submitted to Proc. of the International Workshop `Classical and Quantum Integrable Systems', Dubna, July 1996

Scientific paper

10.1142/S0217751X97000037

Integrable models of dilaton gravity coupled to electromagnetic and scalar matter fields in dimensions 1+1 and 0+1 are briefly reviewed. The 1+1 dimensional integrable models are either solved in terms of explicit quadratures or reduced to the classically integrable Liouville equation. The 0+1 dimensional integrable models emerge as sectors in generally non integrable 1+1 dimensional models and can be solved in terms of explicit quadratures. The Hamiltonian formulation and the problem of quantizing are briefly discussed. Applications to gravity in any space - time dimension are outlined and a generalization of the so called `no - hair' theorem is proven using local properties of the Lagrange equations for a rather general 1+1 dimensional dilaton gravity coupled to matter. This report is based on the paper hep-th/9605008 but some simplifications, corrections and new results are added.

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