ON NON-RIEMANNIAN PARALLEL TRANSPORT IN REGGE CALCULUS

We discuss the possibility of incorporating non-Riemannian parallel transport into Regge calculus. It is shown that every Regge lattice is locally equivalent to a space of constant curvature. Therefore well known-concepts of differential geometry imply the definition of an arbitrary linear affine connection on a Regge lattice.Comment: 12 pages, Plain-TEX, two figures (available from the author

A teleparallel model for the neutrino

The main result of the paper is a new representation for the Weyl Lagrangian (massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e. an orthonormal tetrad of covector fields. We write down a simple Lagrangian - wedge product of axial torsion with a lightlike element of the coframe - and show that variation of the resulting action with respect to the coframe produces the Weyl equation. The advantage of our approach is that it does not require the use of spinors, Pauli matrices or covariant differentiation. The only geometric concepts we use are those of a metric, differential form, wedge product and exterior derivative. Our result assigns a variational meaning to the tetrad representation of the Weyl equation suggested by J.B.Griffiths and R.A.Newing.Comment: 4 pages, REVTe

Weyl's Lagrangian in teleparallel form

The main result of the paper is a new representation for the Weyl Lagrangian (massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e. an orthonormal tetrad of covector fields. We write down a simple Lagrangian - wedge product of axial torsion with a lightlike element of the coframe - and show that this gives the Weyl Lagrangian up to a nonlinear change of dynamical variable. The advantage of our approach is that it does not require the use of spinors, Pauli matrices or covariant differentiation. The only geometric concepts we use are those of a metric, differential form, wedge product and exterior derivative. Our result assigns a variational meaning to the tetrad representation of the Weyl equation suggested by J. B. Griffiths and R. A. Newing

Gravity on a parallelizable manifold. Exact solutions

The wave type field equation \square \vt^a=\la \vt^a, where \vt^a is a coframe field on a space-time, was recently proposed to describe the gravity field. This equation has a unique static, spherical-symmetric, asymptotically-flat solution, which leads to the viable Yilmaz-Rosen metric. We show that the wave type field equation is satisfied by the pseudo-conformal frame if the conformal factor is determined by a scalar 3D-harmonic function. This function can be related to the Newtonian potential of classical gravity. So we obtain a direct relation between the non-relativistic gravity and the relativistic model: every classical exact solution leads to a solution of the field equation. With this result we obtain a wide class of exact, static metrics. We show that the theory of Yilmaz relates to the pseudo-conformal sector of our construction. We derive also a unique cosmological (time dependent) solution of the described type.Comment: Latex, 17 page

A gauge theoretical view of the charge concept in Einstein gravity

We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict definition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably find that the gravitational coupling constant has dimension $\hbar/l^2$, the mass parameter of a particle dimension $\hbar/l$, and the Schwarzschild mass parameter dimension l (where l means length). These dimensions confirm the meaning of mass as elementary and as monopole charge of the translation group, respectively. In detail, we find that the Schwarzschild mass parameter is a quasi-electric monopole charge of the time translation whereas the NUT parameter is a quasi-magnetic monopole charge of the time translation as well as a topological charge. The Kerr parameter and the electric and magnetic charges are interpreted similarly. We conclude that each elementary charge of a Casimir operator of the gauge group is the source of a (quasi-electric) monopole charge of the respective Killing vector.Comment: LaTeX2e, 16 pages, 1 figure; enhanced discussio

Regge Calculus in Teleparallel Gravity

In the context of the teleparallel equivalent of general relativity, the Weitzenbock manifold is considered as the limit of a suitable sequence of discrete lattices composed of an increasing number of smaller an smaller simplices, where the interior of each simplex (Delaunay lattice) is assumed to be flat. The link lengths between any pair of vertices serve as independent variables, so that torsion turns out to be localized in the two dimensional hypersurfaces (dislocation triangle, or hinge) of the lattice. Assuming that a vector undergoes a dislocation in relation to its initial position as it is parallel transported along the perimeter of the dual lattice (Voronoi polygon), we obtain the discrete analogue of the teleparallel action, as well as the corresponding simplicial vacuum field equations.Comment: Latex, 10 pages, 2 eps figures, to appear in Class. Quant. Gra

Einstein-aether theory, violation of Lorentz invariance, and metric-affine gravity

We show that the Einstein-aether theory of Jacobson and Mattingly (J&M) can be understood in the framework of the metric-affine (gauge theory of) gravity (MAG). We achieve this by relating the aether vector field of J&M to certain post-Riemannian nonmetricity pieces contained in an independent linear connection of spacetime. Then, for the aether, a corresponding geometrical curvature-square Lagrangian with a massive piece can be formulated straightforwardly. We find an exact spherically symmetric solution of our model.Comment: Revtex4, 38 pages, 1 figur

Torsion and the Gravitational Interaction

By using a nonholonomous-frame formulation of the general covariance principle, seen as an active version of the strong equivalence principle, an analysis of the gravitational coupling prescription in the presence of curvature and torsion is made. The coupling prescription implied by this principle is found to be always equivalent with that of general relativity, a result that reinforces the completeness of this theory, as well as the teleparallel point of view according to which torsion does not represent additional degrees of freedom for gravity, but simply an alternative way of representing the gravitational field.Comment: Version 2: minor presentation changes, a reference added, 11 pages (IOP style

Solvent contribution to the stability of a physical gel characterized by quasi-elastic neutron scattering

The dynamics of a physical gel, namely the Low Molecular Mass Organic Gelator {\textit Methyl-4,6-O-benzylidene-$\alpha$ -D-mannopyranoside ($\alpha$-manno)} in water and toluene are probed by neutron scattering. Using high gelator concentrations, we were able to determine, on a timescale from a few ps to 1 ns, the number of solvent molecules that are immobilised by the rigid network formed by the gelators. We found that only few toluene molecules per gelator participate to the network which is formed by hydrogen bonding between the gelators' sugar moieties. In water, however, the interactions leading to the gel formations are weaker, involving dipolar, hydrophobic or $\pi-\pi$ interactions and hydrogen bonds are formed between the gelators and the surrounding water. Therefore, around 10 to 14 water molecules per gelator are immobilised by the presence of the network. This study shows that neutron scattering can give valuable information about the behaviour of solvent confined in a molecular gel.Comment: Langmuir (2015

Nonequilibrium thermodynamics as a gauge theory

We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential. A widely accepted expression for the total entropy production of a system arises as the simplest gauge-invariant completion of the time derivative of Gibbs's entropy. We show that transition rates can be given a simple physical characterization in terms of locally-detailed-balanced heat reservoirs. It follows that Clausius's measure of irreversibility along a cyclic transformation is a geometric phase. In this picture, the gauge symmetry arises as the arbitrariness in the choice of a prior probability. Thermostatics depends on the information that is disposable to an observer; thermodynamics does not.Comment: 6 pages. Non-fatal errors in eq.(6), eq.(26) and eq.(31) have been amende