Solutions in self-dual gravity constructed via chiral equations.
نویسندگان
چکیده
The chiral model for self-dual gravity given by Husain in the context of the chiral equations approach is discussed. A Lie algebra corresponding to a finite dimensional subgroup of the group of symplectic diffeomorphisms is found, and then use for expanding the Lie algebra valued connections associated with the chiral model. The self-dual metric can be explicitly given in terms of harmonic maps and in terms of a basis of this subalgebra. PACS numbers: 04.20.Fy, 04.20.Jb, 11.10.Lm
منابع مشابه
Chiral Gravity, Log Gravity, and Extremal CFT
We show that the linearization of all exact solutions of classical chiral gravity around the AdS3 vacuum have positive energy. Non-chiral and negative-energy solutions of the linearized equations are infrared divergent at second order, and so are removed from the spectrum. In other words, chirality is confined and the equations of motion have linearization instabilities. We prove that the only ...
متن کاملSelf-dual Maxwell field in 3D gravity with torsion
We study the system of self-dual Maxwell field coupled to 3D gravity with torsion, with Maxwell field modified by a topological mass term. General structure of the field equations reveals a new, dynamical role of the classical central charges, and gives a simple correspondence between self-dual solutions with torsion and their Riemannian counterparts. We construct two exact self-dual solutions,...
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 کاملYang–Mills equations and gravity
There is remarkable relation between self-dual Yang–Mills and self-dual Einstein gravity in four Euclidean dimensions. Motivated by this we investigate the Spin(7) and G2 invariant self-dual Yang–Mills equations in eight and seven Euclidean dimensions and search for their possible analogs in gravitational theories. The reduction of the self-dual Yang– Mills equations to one dimension results in...
متن کاملSelf - Duality in D ≤ 8 - dimensional Euclidean Gravity
In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Rie-mannian manifold. Solutions to these self-duality equations are provided by manifolds of SU (2), SU (3), G 2 and Spin(7) holonomy. The equations in eight dimensions are a master set for those in lowe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Physical review. D, Particles and fields
دوره 52 8 شماره
صفحات -
تاریخ انتشار 1995