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The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework
Інший ID:
2010 Mathematics Subject Classification: 37K10; 16E45
DOI: http://dx.doi.org/10.3842/SIGMA.2011.118
DOI: http://dx.doi.org/10.3842/SIGMA.2011.118
Посилання:
The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework / A. Dimakis, N. Kanning, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 57 назв. — англ.
Підтримка:
We would like to thank Vladimir S. Manko and anonymous referees for helpful comments.
During the course of this work, N.K. has been at the Max-Planck-Institute for Dynamics and
Self-Organization in G¨ottingen.
Дата:
2011
Переглядів:
513
Завантажень:
269
Анотація:
The non-autonomous chiral model equation for an m×m matrix function on a two-dimensional space appears in particular in general relativity, where for m=2 a certain reduction of it determines stationary, axially symmetric solutions of Einstein's vacuum equations, and for m=3 solutions of the Einstein-Maxwell equations. Using a very simple and general result of the bidifferential calculus approach to integrable partial differential and difference equations, we generate a large class of exact solutions of this chiral model. The solutions are parametrized by a set of matrices, the size of which can be arbitrarily large. The matrices are subject to a Sylvester equation that has to be solved and generically admits a unique solution. By imposing the aforementioned reductions on the matrix data, we recover the Ernst potentials of multi-Kerr-NUT and multi-Deminski-Newman metrics.
