Vacuum Solutions of Classical Gravity on Cyclic Groups from Noncommutative Geometry
نویسنده
چکیده
Based on the observation that the moduli of parallel transports(link variable) on a cyclic group modify the metric on this group, we construct several action functionals for these parallel transports within the framework of noncommutative geometry. After solving the equations of motion, we find that one type of action can give nontrivial vacuum solutions for gravity on this cyclic group in a broad range of coupling constants and that such solutions can be expressed with Chebyshev’s polynomials.
منابع مشابه
Exact Solutions of Noncommutative Vacuum Einstein Field Equations and Plane-fronted Gravitational Waves
We construct a class of exact solutions of the noncommutative vacuum Einstein field equations, which are noncommutative analogues of the plane-fronted gravitational waves in classical gravity.
متن کاملFinsler Black Holes Induced by Noncommutative Anholonomic Distributions in Einstein Gravity
We study Finsler black holes induced from Einstein gravity as possible effects of quantum spacetime noncommutativity. Such Finsler models are defined by nonholonomic frames not on tangent bundles but on (pseudo) Riemannian manifolds being compatible with standard theories of physics. We focus on noncommutative deformations of Schwarzschild metrics into locally anisotropic stationary ones with s...
متن کاملExact Solutions with Noncommutative Symmetries in Einstein and Gauge Gravity
We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such solutions are generated by anholonomic frame transforms and parametrized by generic off–diagonal metrics. For certain particular cases, the new classes of metrics h...
متن کاملIntersecting Connes Noncommutative Geometry with Quantum Gravity
An intersection of Noncommutative Geometry and Loop Quantum Gravity is proposed. Alain Connes’ Noncommutative Geometry provides a framework in which the Standard Model of particle physics coupled to general relativity is formulated as a unified, gravitational theory. However, to this day no quantization procedure compatible with this framework is known. In this paper we consider the noncommutat...
متن کاملMPI-PhT 99-16 April Holography based on noncommutative geometry and the AdS/CFT correspondence
Exponential regularization of orthogonal and Anti-de Sitter (AdS) space is presented based on noncommutative geometry. We show that an adequately adopted noncommutative deformation of geometry makes the holography of higher dimensional quantum theory of gravity and lower dimensional theory possible. Detail counting for observable degrees of freedom of quantum system of gravity in the bulk of no...
متن کامل