Dressing with Control: using integrability to generate desired solutions to Einstein's equations
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Volume
10
Pagination
207 - 231
DOI
10.1007/978-3-319-06722-3_9
Journal
Nonlinear Systems and Complexity
Metadata
Show full item recordAbstract
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, ASCollections
- Mathematics [1234]