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    Dressing with Control: using integrability to generate desired solutions to Einstein's equations 
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    Dressing with Control: using integrability to generate desired solutions to Einstein's equations

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    Accepted Version (310.9Kb)
    Volume
    10
    Pagination
    207 - 231
    DOI
    10.1007/978-3-319-06722-3_9
    Journal
    Nonlinear Systems and Complexity
    Metadata
    Show full item record
    Abstract
    Motivated by integrability of the sine-Gordon equation, we investigate a technique for constructing desired solutions to Einstein's equations by combining a dressing technique with a control-theory approach. After reviewing classical integrability, we recall two well-known Killing field reductions of Einstein's equations, unify them using a harmonic map formulation, and state two results on the integrability of the equations and solvability of the dressing system. The resulting algorithm is then combined with an asymptotic analysis to produce constraints on the degrees of freedom arising in the solution-generation mechanism. The approach is carried out explicitly for the Einstein vacuum equations. Applications of the technique to other geometric field theories are also discussed.
    Authors
    Beheshti, S; Tahvildar-Zadeh, AS
    URI
    http://qmro.qmul.ac.uk/xmlui/handle/123456789/12654
    Collections
    • Mathematics [975]
    Licence information
    http://arxiv.org/abs/1312.5253
    Copyright statements
    © Springer International Publishing Switzerland 2014
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