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A solution for the Einstein gravity coupled with non linear electrodynamics is introduced in 2+1 dimensions. Especially, in the case with a non-vanishing cosmological constant, we obtain a novel black hole solution. To find fundamental…

The solutions of $U(1)$ gauge-gravity coupling is one of the interesting models for analyzing the semi-classical nature of spacetime. In this regard, different well-known singular and nonsingular solutions have been taken into account. The…

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…

Using Fedosov theory of deformation quantization of endomorphism bundle we construct several models of pure geometric, deformed vacuum gravity, corresponding to arbitrary symplectic noncommutativity tensor. Deformations of Einstein-Hilbert…

For a large class of word hyperbolic groups G the cross product C^*-algebra arising from the action of G on its Gromov boundary is shown to satisfy Poincare duality in K-theory. This class strictly contains fundamental groups of compact,…

In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we…

New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these…

All non-equivalent solutions of vacuum Maxwell equations are found for the case when space-time manifolds admit simply transitive four-parameter groups of motions $G_4(N)$. The potentials of the admissible electromagnetic fields admit the…

We briefly review the previous works on the renormalization group in quantum general relativity with the cosmological constant, based on the Vilkovisky and DeWitt version of effective action. On top of that, we discuss the prospects of the…

Higher dimensional, static, cylindrically symmetric vacuum solutions with and without a cosmological constant in the Brans-Dicke theory are presented. We show that, for a negative cosmological constant and for specific values of the…

We present the exact exterior solution for a static and neutral cylindrically symmetric source in locally conformal invariant Weyl gravity. As a special case the general relativity analogue still can be attained, however only as a…

We present a proof for certain cases of the noncommutative Borsuk-Ulam conjectures proposed by Baum, D\k{a}browski, and Hajac. When a unital $C^*$-algebra $A$ admits a free action of $\mathbb{Z}/k\mathbb{Z}$, $k \geq 2$, there is no…

We formulate a Yang-Mills action principle for noncommutative connections on an endomorphism algebra of a vector bundle. It is shown that there is an influence of the topology of the vector bundle onto the structure of the vacuums of the…

We develop the quantization of unimodular gravity in the Plebanski and Ashtekar formulations and show that the quantum effective action defined by a formal path integral is unimodular. This means that the effective quantum geometry does not…

We find a new family of galactic metrics corresponding to flat rotation curves at the outer radii. These are vacuum solutions to a gravity theory where the Newton's coupling varies mildly in space. The effective `mass', whose origin is…

Modified Gravity (MOG) has been used successfully to explain the rotation curves of galaxies, the motion of galaxy clusters, the Bullet Cluster, and cosmological observations without the use of dark matter or Einstein's cosmological…

A non-perturbative and background-independent quantum formulation of quadratic gravity is provided. A canonical quantization procedure introduced in previous works, named after Dirac and Pauli, is here applied to quadratic gravity to…

Assuming that the natural gauge group of gravity is given by the group of isometries of a given space, for a maximally symmetric space we derive a model in which gravity is essentially a gauge theory of translations. Starting from first…

We show the existence of geometric quotients for the spaces of certain classes of morphisms of sheaves on projective space, modulo the canonical action of the group of automorphisms.

We present the state of the art regarding the relation between the physics of Quantum Black Holes and Noncommutative Geometry. We start with a review of models proposed in the literature for describing deformations of General Relativity in…