MGAT1 - Integrability and Solution Generating Methods for Einstein's Field Equations in Four and Higher Dimensions |
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Speaker |
Alekseev, Georgy |
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Talk Title |
Einstein's field equations in the context of theory of integrable systems: from vacuum solitons to integrable field dynamics in string gravity theories |
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Abstract |
In this talk, after some historical remarks, we recall the key-points of Belinski - Zakharov inverse scattering approach and soliton technique for vacuum Einstein equations (1978) and the author's modification of this approach for Einstein - Maxwell fields (1980). Then we describe the integrability structure in spacetimes of any dimensions D>=4 of the symmetry reduced low-energy dynamics of the bosonic sector of heterotic string effective action. For these equations which govern gravitational, dilaton, antisymmetric tensor and any number n of Abelian vector gauge fields, we construct an equivalent (2 d+n)x(2 d+n)-matrix spectral problem (d=D-2), describe different types of soliton generating transformations and outline the monodromy transform approach and linear singular integral equation methods for their solution. |
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