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

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.

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

Spherically Symmetric Solutions in M\o ller's Tetrad Theory of Gravitation

The general solution of M\o ller's field equations in case of spherical symmetry is derived. The previously obtained solutions are verified as special cases of the general solution.Comment: LaTeX2e with AMS-LaTeX 1.2, 8 page

Quantitative Relativistic Effects in the Three-Nucleon Problem

The quantitative impact of the requirement of relativistic invariance in the three-nucleon problem is examined within the framework of Poincar\'e invariant quantum mechanics. In the case of the bound state, and for a wide variety of model implementations and reasonable interactions, most of the quantitative effects come from kinematic factors that can easily be incorporated within a non-relativistic momentum-space three-body code.Comment: 15 pages, 15 figure

Serendipitous discovery of a projected pair of QSOs separated by 4.5 arcsec on the sky

We present the serendipitous discovery of a projected pair of quasi-stellar objects (QSOs) with an angular separation of $\Delta\theta =4.50$ arcsec. The redshifts of the two QSOs are widely different: one, our programme target, is a QSO with a spectrum consistent with being a narrow line Seyfert 1 AGN at $z=2.05$. For this target we detect Lyman-$\alpha$, \ion{C}{4}, and \ion{C}{3]}. The other QSO, which by chance was included on the spectroscopic slit, is a Type 1 QSO at a redshift of $z=1.68$, for which we detect \ion{C}{4}, \ion{C}{3]} and \ion{Mg}{2}. We compare this system to previously detected projected QSO pairs and find that only about a dozen previously known pairs have smaller angular separation.Comment: 4 pages, 3 figures. Accepted for publication in A

Space-time defects and teleparallelism

We consider the class of space-time defects investigated by Puntigam and Soleng. These defects describe space-time dislocations and disclinations (cosmic strings), and are in close correspondence to the actual defects that arise in crystals and metals. It is known that in such materials dislocations and disclinations require a small and large amount of energy, respectively, to be created. The present analysis is carried out in the context of the teleparallel equivalent of general relativity (TEGR). We evaluate the gravitational energy of these space-time defects in the framework of the TEGR and find that there is an analogy between defects in space-time and in continuum material systems: the total gravitational energy of space-time dislocations and disclinations (considered as idealized defects) is zero and infinit, respectively.Comment: 22 pages, no figures, to appear in the Class. Quantum Gravit

Huygens' Principle for the Klein-Gordon equation in the de Sitter spacetime

In this article we prove that the Klein-Gordon equation in the de Sitter spacetime obeys the Huygens' principle only if the physical mass $m$ of the scalar field and the dimension $n\geq 2$ of the spatial variable are tied by the equation $m^2=(n^2-1)/4$. Moreover, we define the incomplete Huygens' principle, which is the Huygens' principle restricted to the vanishing second initial datum, and then reveal that the massless scalar field in the de Sitter spacetime obeys the incomplete Huygens' principle and does not obey the Huygens' principle, for the dimensions $n=1,3$, only. Thus, in the de Sitter spacetime the existence of two different scalar fields (in fact, with m=0 and $m^2=(n^2-1)/4$), which obey incomplete Huygens' principle, is equivalent to the condition $n=3$ (in fact, the spatial dimension of the physical world). For $n=3$ these two values of the mass are the endpoints of the so-called in quantum field theory the Higuchi bound. The value $m^2=(n^2-1)/4$ of the physical mass allows us also to obtain complete asymptotic expansion of the solution for the large time. Keywords: Huygens' Principle; Klein-Gordon Equation; de Sitter spacetime; Higuchi Boun

ALLSMOG: an APEX Low-redshift Legacy Survey for MOlecular Gas. I - molecular gas scaling relations, and the effect of the CO/H2 conversion factor

We present ALLSMOG, the APEX Low-redshift Legacy Survey for MOlecular Gas. ALLSMOG is a survey designed to observe the CO(2-1) emission line with the APEX telescope, in a sample of local galaxies (0.01 < z < 0.03), with stellar masses in the range 8.5 < log(M*/Msun) < 10. This paper is a data release and initial analysis of the first two semesters of observations, consisting of 42 galaxies observed in CO(2-1). By combining these new CO(2-1) emission line data with archival HI data and SDSS optical spectroscopy, we compile a sample of low-mass galaxies with well defined molecular gas masses, atomic gas masses, and gas-phase metallicities. We explore scaling relations of gas fraction and gas consumption timescale, and test the extent to which our findings are dependent on a varying CO/H2 conversion factor. We find an increase in the H2/HI mass ratio with stellar mass which closely matches semi-analytic predictions. We find a mean molecular gas fraction for ALLSMOG galaxies of MH2/M* = (0.09 - 0.13), which decreases with stellar mass. We measure a mean molecular gas consumption timescale for ALLSMOG galaxies of 0.4 - 0.7 Gyr. We also confirm the non-universality of the molecular gas consumption timescale, which varies (with stellar mass) from ~100 Myr to ~2 Gyr. Importantly, we find that the trends in the H2/HI mass ratio, gas fraction, and the non-universal molecular gas consumption timescale are all robust to a range of recent metallicity-dependent CO/H2 conversion factors.Comment: 25 pages, 15 figures. Accepted for publication in MNRA

Gravitational Energy-Momentum Density in Teleparallel Gravity

In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz transformations. By rewriting the gauge gravitational field equation in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equation, and the gauge current reduces to the M{\o}ller's canonical energy-momentum density of the gravitational field.Comment: RevTeX, 4 pages, no figures, to appear in Phys. Rev. Let