Related papers: Nonholomic Distributions and Gauge Models of Einst…
A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a…
We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be…
A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their…
Nonholonomic distributions and adapted fame structures on (pseudo) Riemannian manifolds of even dimension are employed to build structures equivalent to almost Kahler geometry and which allows to perform a Fedosov-like quantization of…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
We argue that the Einstein gravity theory can be reformulated in almost Kahler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of…
We develop an approach to the theory nonholonomic relativistic stochastic processes on curved spaces. The Ito and Stratonovich calculus are formulated for spaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting…
The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Ho\vrava-Lifshits, HL; Einstein--Finsler gravity extensions etc) posses an important decoupling property with respect to…
Various types of Lagrange and Finsler geometries and the Einstein gravity theory, and modifications, can be modelled by nonholonomic distributions on tangent bundles/ manifolds when the fundamental geometric objects are adapted to nonlinear…
We model pseudo-Finsler geometries, with pseudo-Euclidean signatures of metrics, for two classes of four dimensional nonholonomic manifolds: a) tangent bundles with two dimensional base manifolds and b) pseudo-Riemannian/ Einstein…
Off-diagonal vacuum and nonvacuum configurations in Einstein gravity can mimic physical effects of modified gravitational theories of $f(R,T,R_{\mu \nu}T^{\mu \nu})$ type. To prove this statement, exact and approximate solutions are…
We present a generalization of the spinor and twistor geometry for on (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler-Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors…
We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…
We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x,t]=\lambda x drastically reduce the moduli of possible metrics g up to normalisation to a…
In this work, we apply the anholonomic deformation method for constructing new classes of anisotropic cosmological solutions in Einstein gravity and/or generalizations with nonholonomic variables. There are analyzed four types of, in…
Certain off-diagonal vacuum and nonvacuum configurations in Einstein gravity can mimic physical effects of modified gravitational theories of $ f(R,T,R_{\mu\nu}T^{\mu\nu})$ type. We prove this statement by constructing exact and approximate…
We investigate bi-Hamiltonian structures and mKdV hierarchies of solitonic equations generated by (semi) Riemannian metrics and curve flows of non-stretching curves. There are applied methods of the geometry of nonholonomic manifolds…
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…
In the literature, there are several papers establishing a correspondence between a deformed kinematics and a nontrivial (momentum dependent) metric. In this work, we study in detail the relationship between the trajectories given by a…
We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest…