Energy and angular momentum of general 4-dimensional stationary axi-symmetric spacetime in teleparallel geometry

We derive an exact general axi-symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation. The solution is characterized by four parameters $M$ (mass), $Q$ (charge), $a$ (rotation) and $L$ (NUT). We then, calculate the total exterior energy using the energy-momentum complex given by M{\o}ller in the framework of Weitzenb$\ddot{o}$ck geometry. We show that the energy contained in a sphere is shared by its interior as well as exterior. We also calculate the components of the spatial momentum to evaluate the angular momentum distribution. We show that the only non-vanishing components of the angular momentum is in the Z direction.Comment: Latex. Will appear in IJMP

Relativity accommodates superluminal mean velocities

Contrary to a widespread belief, measures of velocity can yield a value larger than $c$, the instantaneous light speed in vacuum, without contradicting Einstein's relativity. Nevertheless, the effect turns out to be too small to explain the recently claimed superluminal velocity by the OPERA collaboration. Several other general relativistic effects acting on the OPERA neutrinos are also analyzed. All of them are unable to explain the OPERA result.Comment: 5 pages; Latex source, 2 eps figures (expanded discussion, a few typos corrected, some refs. added

Isometric Immersions and the Waving of Flags

In this article we propose a novel geometric model to study the motion of a physical flag. In our approach a flag is viewed as an isometric immersion from the square with values into $\mathbb R^3$ satisfying certain boundary conditions at the flag pole. Under additional regularity constraints we show that the space of all such flags carries the structure of an infinite dimensional manifold and can be viewed as a submanifold of the space of all immersions. The submanifold result is then used to derive the equations of motion, after equipping the space of isometric immersions with its natural kinetic energy. This approach can be viewed in a similar spirit as Arnold's geometric picture for the motion of an incompressible fluid.Comment: 25 pages, 1 figur

Kerr-Newman Solution and Energy in Teleparallel Equivalent of Einstein Theory

An exact charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the teleparallel equivalent of Einstein theory is derived. It is characterized by three parameters ``$$the gravitational mass $M$, the charge parameter $Q$ and the rotation parameter $a$" and its associated metric gives Kerr-Newman spacetime. The parallel vector field and the electromagnetic vector potential are axially symmetric. We then, calculate the total energy using the gravitational energy-momentum. The energy is found to be shared by its interior as well as exterior. Switching off the charge parameter we find that no energy is shared by the exterior of the Kerr-Newman black hole.Comment: 11 pages, Latex. Will appear in Mod. Phys. Lett.

On the Clock Paradox in the case of circular motion of the moving clock

In this paper we deal analytically with a version of the so called clock paradox in which the moving clock performs a circular motion of constant radius. The rest clock is denoted as (1), the rotating clock is (2), the inertial frame in which (1) is at rest and (2) moves is I and, finally, the accelerated frame in which (2) is at rest and (1) rotates is A. By using the General Theory of Relativity in order to describe the motion of (1) as seen in A we will show the following features. I) A differential aging between (1) and (2) occurs at their reunion and it has an absolute character, i.e. the proper time interval measured by a given clock is the same both in I and in A. II) From a quantitative point of view, the magnitude of the differential aging between (1) and (2) does depend on the kind of rotational motion performed by A. Indeed, if it is uniform there is no any tangential force in the direction of motion of (2) but only normal to it. In this case, the proper time interval reckoned by (2) does depend only on its constant velocity v=romega. On the contrary, if the rotational motion is uniformly accelerated, i.e. a constant force acts tangentially along the direction of motion, the proper time intervals $do depend$ on the angular acceleration alpha. III) Finally, in regard to the sign of the aging, the moving clock (2) measures always a $shorter$ interval of proper time with respect to (1).Comment: LaTex2e, 9 pages, no figures, no tables. It is the follow-on of the paper physics/040503

Transverse radiation force in a tailored optical fiber

We show, by means of simple model calculations, how a weak laser beam sent through an optical fiber exerts a transverse radiation force if there is an azimuthal asymmetry present in the fiber such that one side has a slightly different refractive index than the other. The refractive index difference $\Delta n$ needs only to be very small, of order $10^{-3}$, in order to produce an appreciable transverse displacement of order 10 microns. We argue that the effect has probably already been seen in a recent experiment of She et al. [Phys. Rev. Lett. 101, 243601 (2008)], and we discuss correspondence between these observations and the theory presented. The effect could be used to bend optical fibers in a predictable and controlled manner and we propose that it could be useful for micron-scale devices.Comment: 4 pages, 3 figures. Accepted for publication as Rapid Communication in Phys. Rev.

Simple Model for Wet Granular Materials with Liquid Clusters

We propose a simple phenomenological model for wet granular media to take into account many particle interaction through liquid in the funicular state as well as two-body cohesive force by a liquid bridge in the pendular state. In the wet granular media with small liquid content, liquid forms a bridge at each contact point, which induces two-body cohesive force due to the surface tension. As the liquid content increases, some liquid bridges merge, and more than two grains interact through a single liquid cluster. In our model, the cohesive force acts between the grains connected by a liquid-gas interface. As the liquid content increases, the number of grains that interact through the liquid increases, but the liquid-gas interface may decrease when liquid clusters are formed. Due to this competition, our model shows that the shear stress has a maximum as a function of the liquid-content.Comment: 6 pages, 8 figures. Discussion is updated. Accepted for publication in EP

Scaling Laws in High-Energy Inverse Compton Scattering. II. Effect of Bulk Motions

We study the inverse Compton scattering of the CMB photons off high-energy nonthermal electrons. We extend the formalism obtained by the previous paper to the case where the electrons have non-zero bulk motions with respect to the CMB frame. Assuming the power-law electron distribution, we find the same scaling law for the probability distribution function P_{1,K}(s) as P_{1}(s) which corresponds to the zero bulk motions, where the peak height and peak position depend only on the power-index parameter. We solved the rate equation analytically. It is found that the spectral intensity function also has the same scaling law. The effect of the bulk motions to the spectral intensity function is found to be small. The present study will be applicable to the analysis of the X-ray and gamma-ray emission models from various astrophysical objects with non-zero bulk motions such as radio galaxies and astrophysical jets.Comment: 10 pages, 3 figures, accepted version by Physical Review

New Measure of the Dissipation Region in Collisionless Magnetic Reconnection

A new measure to identify a small-scale dissipation region in collisionless magnetic reconnection is proposed. The energy transfer from the electromagnetic field to plasmas in the electron's rest frame is formulated as a Lorentz-invariant scalar quantity. The measure is tested by two-dimensional particle-in-cell simulations in typical configurations: symmetric and asymmetric reconnection, with and without the guide field. The innermost region surrounding the reconnection site is accurately located in all cases. We further discuss implications for nonideal MHD dissipation

Including changes in security of supply in cost benefit analysis – an application to oil prices in the transport sector

This paper contains a tentative suggestion of how to take into account changes in security of supply in real world cost-benefit analysis. Assuming that consumers are risk avers, security of supply can be viewed as a matter of avoiding oscillations in consumption originating from volatile prices of for in- stance oil. When the government makes transport related choices on behalf of the consumers, the effect on oscillations in general consumption should be included in the policy assessment taking into account the most significant correlations between prices on alternative fuels and between fuel prices and consumption in general. In the paper, a method of valuing changes in security of supply based on portfolio theory is applied to some very simple transport related examples. They indicate that includ- ing the value of changes in security of supply often makes very little difference to the results of cost benefit analysis, but more work has to be done on quantifying, among other things, consumers’ risk aversion and the background standard deviation in total consumption before firm conclusions can be drawn