Related papers: Two-Connection Renormalization and Nonholonomic Ga…
Gravity is perturbatively renormalizable for the physical states which can be conveniently defined via foliation-based quantization. In recent sequels, one-loop analysis was explicitly carried out for Einstein-scalar and Einstein-Maxwell…
The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…
We study two--loop renormalization in $(2+\epsilon)$--dimensional quantum gravity. As a first step towards the full calculation, we concentrate on the divergences which are proportional to the number of matter fields. We calculate the…
We study the essential renormalization group equation, in which inessential couplings are removed via field redefinitions, for Einstein gravity coupled to a massive scalar field in the presence of a cosmological constant. Our results…
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…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
We discuss some of the issues to be addressed in arriving at a definitive noncommutative Riemannian geometry that generalises conventional geometry both to the quantum domain and to the discrete domain. This also provides an introduction to…
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 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…
Based on the view that Einstein's theory can be interpreted as a gauge theory of Lorentz group, we decompose the gravitational connection (the gauge potential of Lorentz group) $\vGm_\mu$ into the restricted connection made of the potential…
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…
Motivated by the apparent dependence of string $\sigma$--models on the sum of spacetime metric and antisymmetric tensor fields, we reconsider gravity theories constructed from a nonsymmetric metric. We first show that all such "geometrical"…
The quantum gauge general relativity is proposed in the framework of quantum gauge theory of gravity. It is formulated based on gauge principle which states that the correct symmetry for gravitational interactions should be gravitational…
The quantum gravity is formulated based on gauge principle. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge potential. A preliminary study on gravitational gauge group…
We evaluate the quantum corrections of the Einstein-Hilbert action with boundaries in the $2+\epsilon$ dimensional expansion approach. We find the Einstein-Hilbert action with boundaries to be renormalizable to the one loop order. We…
We review and extend in several directions recent results on the asymptotic safety approach to quantum gravity. The central issue in this approach is the search of a Fixed Point having suitable properties, and the tool that is used is a…
Using the Batalin-Vilkovisky technique and the background field method the proof of gauge invariant renormalizability is elaborated for a generic model of quantum gravity which is diffeomorphism invariant and has no other, potentially…
Cylindrical gravitational waves of Einstein gravity are described by an integrable system (Ernst system) whose quantization is a long standing problem. We propose to bootstrap the quantum theory along the following lines: The quantum theory…
We study the functional renormalization group equation and its solutions of the gravity having the background matters. From the system equivalence eliminating vacuum divergence, we are confirmed to give Newton coupling. We also give the…
A modified Einstein-Gauss-Bonnet gravity in four dimensions where the quadratic Gauss-Bonnet term is coupled to a scalar field is considered. The field equations of the model are obtained by variational methods by making use of the…