منابع مشابه
Integrable Deformations of Self Dual Gravity
A proposal for constructing a universal nonlinear Ŵ∞ algebra is made as the symmetry algebra of a rotational Killing-symmetry reduction of the nonlinear perturbations of Moyal-Integrable deformations of D = 4 Self Dual Gravity (IDSDG). This is attained upon the construction of a nonlinear bracket based on nonlinear gauge theories associated with infinite dimensional Lie algebras. A Quantization...
متن کاملFrom 2D Integrable Systems to Self-Dual Gravity
We explain how to construct solutions to the self-dual Einstein vacuum equations from solutions of various two-dimensional integrable systems by exploiting the fact that the Lax formulations of both systems can be embedded in that of the self-dual Yang–Mills equations. We illustrate this by constructing explicit self-dual vacuum metrics on R × Σ, where Σ is a homogeneous space for a real subgro...
متن کاملIntegrable Field Theories derived from 4D Self-dual Gravity
We reformulate the self-dual Einstein equation as a trio of di erential form equations for simple two-forms. Using them, we can quickly show the equivalence of the theory and 2D sigma models valued in in nite-dimensional group, which was shown by Park and Husain earlier. We also derive other eld theories including the 2D Higgs bundle equation. This formulation elucidates the relation among thos...
متن کاملSpherically Symmetric Gravity as a Completely Integrable System ∗
It is shown-in Ashtekar's canonical framework of General Rel-ativity-that spherically symmetric (Schwarzschild) gravity in 4 dimensional space-time constitutes a finite dimensional completely inte-grable system. Canonically conjugate observables for asymptotically flat space-times are masses as action variables and-surprisingly-time variables as angle variables, each of which is associated with...
متن کاملOn self-dual gravity.
We study the Ashtekar-Jacobson-Smolin equations that characterise four dimensional complex metrics with self-dual Riemann tensor. We find that we can characterise any self-dual metric by a function that satisfies a non-linear evolution equation, to which the general solution can be found iteratively. This formal solution depends on two arbitrary functions of three coordinates. We construct expl...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2008
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/41/39/395206