Related papers: Four Dimensional Elasticity and General Relativity
Extra dimensions can be utilized to simplify problems in classical mechanics, offering new insights. Here we show a simple example of how the motion of a test particle under the influence of an inverse-quadratic potential in 1D is…
Term "asymmetrical pseudoelasticity" refers to the theory, in which a symmetrical stress tensor and a symmetrical strain tensor are connected by means of an asymmetrical material tensor. An 6-dimensional asymmetrical matrix of elasticity…
Regge-Teitelboim embedding gravity is the modified gravity based on a simple string-inspired geometrical principle: our spacetime is considered here as a 4-dimensional surface in a flat bulk. This theory is similar to the recently popular…
Acceleration of the universe might be driven by a continuous elastic medium -- elastic dark energy (Bucher and Spergel 1999). Elastic dark energy can stably support equations of state with pressure to energy ratio w > -4/3. Stable expansion…
We suggest an alternative mathematical model for the electron in dimension 1+2. We think of our (1+2)-dimensional spacetime as an elastic continuum whose material points can experience no displacements, only rotations. This framework is a…
General relativity is extended by promoting the three-dimensional gravitational Chern-Simons term to four dimensions. This entails choosing an embedding coordinate v_\mu -- an external quantity, which we fix to be a non-vanishing constant…
Holography has provided valuable insights into the time evolution of strongly coupled gauge theories in a fixed spacetime. However, this framework is insufficient if this spacetime is dynamical. We present a scheme to evolve a…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
A kinetic theory of classical particles serves as a unified basis for developing a geometric $3+1$ spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases…
We extend the classical general relativistic theory of measurement to include the possibility of existence of higher dimensions. The intrusion of these dimensions in the spacetime interval implies that the inertial mass of a particle in…
Effective 4-dimensional theories are investigated which were obtained under dimensional reduction of multidimensional cosmological models with a minimal coupled scalar field as matter source. Conditions for the internal space stabilization…
We present the foundations of a projective geometric theory of elasticity, as well as outline a few possible application possibilities. We give the description of the Cauchy stress and infinitesimal strain tensors compatible with coordinate…
Several attempts to construct theories of gravity with variable mass are considered. The theoretical impacts of allowing the rest mass to vary with respect to time or an appropriate curve parameter are examined in the framework of Newtonian…
Preliminary results on a canonical formulation of general relativity based on an analogy with the string model of elementary particles are presented. Rather than the metric components, the basic fields of the formalism are taken to be the…
Can global internal and spacetime symmetries be connected without supersymmetry? To answer this question, we investigate Minkowski spacetimes with d space-like extra dimensions and point out under which general conditions external…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…
A part of relativistic dynamics (or mechanics) is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented,…
Analogue spacetimes can be used to probe and study physically interesting spacetime geometries by constructing, either theoretically or experimentally, some notion of an effective Lorentzian metric $[g_\mathrm{eff}(g,V,\,\Xi)]_{ab}$. These…
Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a…