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We consider numerical black hole solutions in the Weyl conformal geometry, and its associated conformally invariant Weyl quadratic gravity. In this model Einstein gravity (with a positive cosmological constant) is recovered in the…
By constructing a model of spacetime having a strong curvature singularity in which causal geodesics are complete, but more generic causal curves are not, we explicitly show that some electrostatic field configurations on that background…
Noncommutative U(1) gauge theory on the Moyal-Weyl space ${\bf R}^2{\times}{\bf R}^2_{\theta}$ is regularized by approximating the noncommutative spatial slice ${\bf R}^2_{\theta}$ by a fuzzy sphere of matrix size $L$ and radius $R$ .…
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
On the basis of the Lorentz equations of motion, the orbit of a charge driven by a generic E.M. field with planar symmetry is formulated and analyzed within the framework of a Lorentzian geometry with a curvature whose order of magnitude is…
We find the Noether point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries are composed of a quasi-invariance transformation, a time-dependent rotation and a time-dependent spatial translation. The…
We determine the local structure of all pseudo-Riemannian manifolds $(M,g)$ in dimensions $n\ge4$ whose Weyl conformal tensor $W$ is parallel and has rank 1 when treated as an operator acting on exterior 2-forms at each point. If one fixes…
The Wick rotation in quantum field theory is considered in terms of analytical continuation in the signature matrix parameter w = eta_00. Regularization of propagators by a complex metric parameter in most cases preserves (i) the…
This paper presents a systematical study of stationary (rotating) cylindrical space-times of a Weyl form that are solutions to D=4 Einstein-Maxwell equations with cosmological constant. The corresponding equations of motion - with zero…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
The study deals with a minimal energy problem in the presence of an external field over noncompact classes of vector measures of infinite dimension in a locally compact space. The components are positive measures (charges) satisfying…
Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations…
A class of harmonic solutions to the steady Euler equations for incompressible fluids is presented in two dimensions in circular, elliptic and bipolar coordinates. Since the velocity field is solenoidal in this case, it can be written as…
The symplectic geometry of the phase space associated with a charged particle is determined by the addition of the Faraday 2-form to the standard structure on the Euclidean phase space. In this paper we describe the corresponding algebra of…
We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the existence of dark matter, is the result of the dynamical evolution of particles in a Weyl type…
We discuss a large class of conformally invariant curvature energies for immersed hypersurfaces of dimension 4. The class under study includes various examples that have appeared in the recent literature and which arise from different…
In recent works, a framework has been developed to describe (quantum) deformed, spherically symmetric and static black holes in four dimensions. The key idea of this so-called Effective Metric Description (EMD) is to parametrise…