Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations
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| Creator |
Dimakis, A.
Müller-Hoissen, F. |
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| Description |
We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-type transformation. This is then applied to the non-autonomous chiral model, a certain reduction of which is known to appear in the case of the D-dimensional vacuum Einstein equations with D−2 commuting Killing vector fields. A large class of exact solutions is obtained, and the aforementioned reduction is implemented. This results in an alternative to the well-known Belinski-Zakharov formalism. We recover relevant examples of space-times in dimensions four (Kerr-NUT, Tomimatsu-Sato) and five (single and double Myers-Perry black holes, black saturn, bicycling black rings).
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| Date |
2019-02-19T18:58:49Z
2019-02-19T18:58:49Z 2013 |
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| Type |
Article
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| Identifier |
Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 80 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 37K10; 16E45 DOI: http://dx.doi.org/10.3842/SIGMA.2013.009 http://dspace.nbuv.gov.ua/handle/123456789/149219 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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