The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework
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 Ein...
Збережено в:
| Дата: | 2011 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148083 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148083 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1480832019-02-17T01:25:45Z The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework Dimakis, A. Kanning, N. Müller-Hoissen, F. 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. 2011 Article 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. 1815-0659 2010 Mathematics Subject Classification: 37K10; 16E45 DOI: http://dx.doi.org/10.3842/SIGMA.2011.118 http://dspace.nbuv.gov.ua/handle/123456789/148083 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Dimakis, A. Kanning, N. Müller-Hoissen, F. |
| spellingShingle |
Dimakis, A. Kanning, N. Müller-Hoissen, F. The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Dimakis, A. Kanning, N. Müller-Hoissen, F. |
| author_sort |
Dimakis, A. |
| title |
The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework |
| title_short |
The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework |
| title_full |
The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework |
| title_fullStr |
The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework |
| title_full_unstemmed |
The Non-Autonomous Chiral Model and the Ernst Equation of General Relativity in the Bidifferential Calculus Framework |
| title_sort |
non-autonomous chiral model and the ernst equation of general relativity in the bidifferential calculus framework |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148083 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT dimakisa thenonautonomouschiralmodelandtheernstequationofgeneralrelativityinthebidifferentialcalculusframework AT kanningn thenonautonomouschiralmodelandtheernstequationofgeneralrelativityinthebidifferentialcalculusframework AT mullerhoissenf thenonautonomouschiralmodelandtheernstequationofgeneralrelativityinthebidifferentialcalculusframework AT dimakisa nonautonomouschiralmodelandtheernstequationofgeneralrelativityinthebidifferentialcalculusframework AT kanningn nonautonomouschiralmodelandtheernstequationofgeneralrelativityinthebidifferentialcalculusframework AT mullerhoissenf nonautonomouschiralmodelandtheernstequationofgeneralrelativityinthebidifferentialcalculusframework |
| first_indexed |
2023-05-20T17:29:14Z |
| last_indexed |
2023-05-20T17:29:14Z |
| _version_ |
1796153406140710912 |