Related papers: Four Dimensional Elasticity and General Relativity
Starting from a model of an elastic medium, we derive equations of motion that are identical in form to Dirac's equation for a spin 1/2 particle with mass, coupled to electromagnetic and gravitational interactions. The mass and…
The notion of ``fundamental constant'' is heavily theory-laden. A natural, fairly precise formulation is possible in the context of the standard model (here defined to include gravity). Some fundamental constants have profound geometric…
In gravitational theories with extra dimensions, it is argued that the existence of a positive vacuum energy generically implies catastrophic instability of our four-dimensional world. The most generic instability is a decompactification…
The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. The equations of motion and stress-energy-momentum tensor for a hyperelastic body are derived from the gauge-invariant action…
A kinetic theory of relativistic gases in a two-dimensional space is developed in order to obtain the equilibrium distribution function and the expressions for the fields of energy per particle, pressure, entropy per particle and heat…
A simple visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean 4-space to yield accurate visualizations as…
Variational principle for a solid in classical mechanics is formulated in terms of a thin elastic 4D bar strain in Minkowsky events space of special relativity. It is shown, that the sum of elastic 4-energies of weak twist and bending under…
The dynamics of defect excitations in crystalline solids is necessary to understand the macroscopic low-energy properties of elastic media. We use fracton-elasticity duality to systematically study the defect dynamics and interactions in…
Main objective of the present dissertation is the investigation for all the possible low energy models which emerge in four dimensions by the dimensional reduction of a gauge theory over multiple connected coset spaces. The higher…
We propose a model for thermo-elastic beams, consistent with the theory of linear three-dimensional thermo-elasticity and deduced by a suitable version of the Principle of Virtual Powers. Dimensional reduction is achieved by postulating…
Minkowski spacetime is a convenient setting for the study of the relativistic dynamics of particles and fields in the vacuum. In order to study events that occur in a dielectric or other linear medium, we adopt the familiar continuum…
We argue that four-dimensional quantum gravity may be essentially renormalizable if one relaxes the assumption of metricity of the theory. We work with Plebanski formulation of general relativity in which the metric (tetrad), the…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
A string theory in $3$ euclidean spacetime dimensions is found to describe the semiclassical behavior of a certain exact physical state of quantum general relativity in $4$ dimensions. Both the worldsheet and the three dimensional metric…
General Relativity extended through a dynamical scalar quartet is proposed as a theory of the scalar-vector-tensor gravity, generically describing the unified gravitational dark matter (DM) and dark energy (DE). The implementation in the…
Metric mean dimension is a geometric invariant of dynamical systems with infinite topological entropy. We relate this concept with the fractal structure of the phase space and the H\"older regularity of the map. Afterwards we improve our…
We show that a topology can be defined in the four dimensional space-time of special relativity so as to obtain a topological semigroup for time. The Minkowski 4-vector character of space-time elements as well as the key properties of…
We show that the dynamics of an elastic solid embedded in a Minkowski space consist of a set of coupled equations describing a spin-1/2 field, $\Psi$, obeying Dirac's equation, a vector potential, $A_\mu$, obeying Maxwell's equations and a…
In this article we propose to add stress-energy tensor to the Einstein equations, assuming that the matter-energy and the metric space-time is nothing but a continuous medium with some elastic properties. We first give a general expression…
Why would anyone wish to generalize the already unappetizing subject of rigid body motion to an arbitrary number of dimensions? At first sight, the subject seems to be both repellent and superfluous. The author will try to argue that an…