Home News About Us Contact Contributors Disclaimer Privacy Policy Help FAQ

Home
Search
Quick Search
Advanced
Fulltext
Browse
Collections
Persons
My eDoc
Session History
Login
Name:
Password:
Documentation
Help
Support Wiki
Direct access to
document ID:


          Display Documents



  history
ID: 575682.0, MPI für Dynamik und Selbstorganisation / Dynamik komplexer Fluide
The non-autonomous chiral model and the Ernst equation of General Relativity in the bidifferential calculus framework
Authors:Dimakis, Aristophanes; Kanning, Nils; Müller-Hoissen, Folkert
Language:English
Date of Publication (YYYY-MM-DD):2011-12-23
Title of Journal:Symmetry, Integrability and Geometry: Methods and Applications
Journal Abbrev.:SIGMA
Volume:7
Sequence Number of Article:118
Review Status:Peer-review
Audience:Experts Only
Abstract / 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.
Free Keywords:bidifferential calculus; chiral model; Ernst equation; Sylvester equation
External Publication Status:published
Document Type:Article
Communicated by:Folkert Müller-Hoissen
Affiliations:MPI für Dynamik und Selbstorganisation/Dynamik komplexer Fluide
External Affiliations:Department of Financial and Management Engineering, University of the Aegean, Chios, Greece
Institute for Mathematics and Institute for Physics, Humboldt University, Berlin, Germany
Identifiers:DOI:10.3842/SIGMA.2011.118
The scope and number of records on eDoc is subject to the collection policies defined by each institute - see "info" button in the collection browse view.