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Inverse Scattering and the Geroch Group

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arxiv 1211.3044 v2 pith:AHXGDGRR submitted 2012-11-13 hep-th gr-qc

Inverse Scattering and the Geroch Group

Despoina Katsimpouri , Axel Kleinschmidt , Amitabh Virmani This is my paper
classification hep-th gr-qc
keywords groupapproachalgebraicgerochinverselinearpurelyscattering
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study the integrability of gravity-matter systems in D=2 spatial dimensions with matter related to a symmetric space G/K using the well-known linear systems of Belinski-Zakharov (BZ) and Breitenlohner-Maison (BM). The linear system of BM makes the group structure of the Geroch group manifest and we analyse the relation of this group structure to the inverse scattering method of the BZ approach in general. Concrete solution generating methods are exhibited in the BM approach in the so-called soliton transformation sector where the analysis becomes purely algebraic. As a novel example we construct the Kerr-NUT solution by solving the appropriate purely algebraic Riemann-Hilbert problem in the BM approach.

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Cited by 3 Pith papers

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