Related papers: Global texture in Lyra geometry
The current race in quantum communication -- endeavouring to establish a global quantum network -- must account for special and general relativistic effects. The well-studied general relativistic effects include Shapiro time-delay,…
Einstein-like Lagrangian field theory is developed to describe elastic solid containing dislocations with finite-sized core. The framework of the Riemann-Cartan geometry in three dimensions is used, and the core self-energy is expressed by…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…
We study inverse problems for the Einstein equations with source fields in a general form. Under a microlocal linearization stability condition, we show that by generating small gravitational perturbations and measuring the responses near a…
We derive a generalized deviation equation in Riemann-Cartan spacetime. The equation describes the dynamics of the connecting vector which links events on two general adjacent world lines. Our result is valid for any theory in a…
We study a class of fourth-order geometric problems modelling Willmore surfaces, conformally constrained Willmore surfaces, isoperimetrically constrained Willmore surfaces, bi-harmonic surfaces in the sense of Chen, among others. We prove…
With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin,…
How do the global properties of a Lorentzian manifold change when endowed with a vector field? This interesting question is tackled in this paper within the framework of Einstein-Aether (EA) theory which has the most general…
This study presents a comprehensive mathematical model for Volterra defects and explores their relations using differential geometry on Riemann--Cartan manifolds. Following the standard Volterra process, we derived the Cartan moving frame,…
The concept of smooth deformations of a Riemannian manifolds, recently evidenced by the solution of the Poincar\'e conjecture, is applied to Einstein's gravitational theory and in particular to the standard FLRW cosmology. We present a…
The present study deals with a spatially homogeneous and anisotropic Bianchi-II cosmological models representing massive strings in normal gauge for Lyra's manifold by applying the variation law for generalized Hubble's parameter that…
We develop a model-independent approach to lagrangian perturbation theory for the large scale structure of the universe. We focus on the displacement field for dark matter particles, and derive its most general structure without assuming a…
We discuss the averaging problem in general relativity, using the form of the macroscopic gravity equations in the case of spherical symmetry in volume preserving coordinates. In particular, we calculate the form of the correlation tensor…
We consider the static elastoplastic theory of dislocations in an elastoplastic material. We use a Yang-Mills type Lagrangian (the teleparallel equivalent of Hilbert-Einstein Lagrangian) and some Lagrangians with anisotropic constitutive…
A scale invariant, Weyl geometric, Lagrangian approach to cosmology is explored, with a a scalar field phi of (scale) weight -1 as a crucial ingredient besides classical matter \cite{Tann:Diss,Drechsler:Higgs}. For a particularly simple…
We initiate the study of Horava-Lifshitz models of gravity in the framework of spectral geometry. As the first step, we calculate the dimension of space-time. It is shown, that for the natural choice of a Dirac operator (or rather…
We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test…
Using the Gauss-Bonnet formula, integral of the Gaussian curvature over a 2-surface enclosed by a curve in the asymptotically flat region of a static spacetime was found to be a measure of a gravitational analogue of Aharonov-Bohm effect by…
We investigate the conditions under which cosmological variations in physical `constants' and scalar fields are detectable on the surface of local gravitationally-bound systems, such as planets, in non-spherically symmetric background…
We study spatial variations of the fine-structure constant in the presence of static straight cosmic strings in the weak-field approximation in Einstein gravity. We work in the context of a generic Bekenstein-type model and consider a gauge…