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Integrable structure of the low-energy string gravity equations in D=4 space-times with two commuting isometries

G. A. Alekseev·M. V. Yurova
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Abstract

The generalized Einstein - Maxwell field equations which arise from a truncated bosonic part of the low - energy string gravity effective action in four dimensions (the so called Einstein-Maxwell - axion - dilaton theory) are considered. The integrable structure of these field equations for D=4 space-times with two commuting isometries is elucidated. We express the dynamical part of the reduced equations as integrability conditions of some overdetermined $4\times 4$-matrix linear system with a spectral parameter. The remaining part of the field equations are expressed as the conditions of existence for this linear system of two $4\times 4$-matrix integrals of special structures. This provides a convenient base for a generalization to these equations of various solution generating methods developed earlier in General Relativity.

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G. A. Alekseev, M. V. Yurova. 2004-01-12. Integrable structure of the low-energy string gravity equations in D=4 space-times with two commuting isometries. https://arxiv.org/abs/hep-th/0401077

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