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

Moving system with speeded-up evolution

In the classical (non-quantum) relativity theory the course of the moving clock is dilated as compared to the course of the clock at rest (the Einstein dilation). Any unstable system may be regarded as a clock. The time evolution (e.g., the decay) of a uniformly moving physical system is considered using the relativistic quantum theory. The example of a moving system is given whose evolution turns out to be speeded-up instead of being dilated. A discussion of this paradoxical result is presented.Comment: 10 pages, LaTe

Elementary analysis of the special relativistic combination of velocities, Wigner rotation, and Thomas precession

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary, which will suit a first course in relativity; (2) intermediate, to suit a second course; and (3) advanced, to suit higher level students. We then give a summary of useful results, and suggest further reading in this often obscure field.Comment: V1: 25 pages, 6 figures; V2: 22 pages, 5 figures. The revised version is shortened and the arguments streamlined. Minor changes in notation and figures. This version matches the published versio

New Path Equations in Absolute Parallelism Geometry

The Bazanski approach, for deriving the geodesic equations in Riemannian geometry, is generalized in the absolute parallelism geometry. As a consequence of this generalization three path equations are obtained. A striking feature in the derived equations is the appearance of a torsion term with a numerical coefficients that jumps by a step of one half from equation to another. This is tempting to speculate that the paths in absolute parallelism geometry might admit a quantum feature.Comment: 4 pages Latex file Journal Reference: Astrophysics and space science 228, 273, (1995

On the Possibility of Measuring the Abraham Force using Whispering Gallery Modes

Critical experimental tests of the time-dependent Abraham force in phenomenological electrodynamics are scarce. In this paper we analyze the possibility of making use of intensity-modulated whispering gallery modes in a microresonator for this purpose. Systems of this kind appear attractive, as the strong concentration of electromagnetic fields near the rim of the resonator serves to enhance the Abraham torque exerted by the field. We analyze mainly spherical resonators, although as an introductory step we consider also the cylinder geometry. The order of magnitude of the Abraham torques are estimated by inserting reasonable values for the various input parameters. As expected, the predicted torques turn out to be very small, although probably not beyond any reach experimentally. Our main idea is essentially a generalization of the method used by G. B. Walker et al. [Can. J. Phys. 53, 2577] for low-frequency fields, to the optical case.Comment: 6 pages, no figures. Minor typos corrected, acknowledgment added. To appear in Phys. Rev.

Energy Content of Colliding Plane Waves using Approximate Noether Symmetries

This paper is devoted to study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use approximate Lie symmetry method of Lagrangian for differential equations. We formulate the first-order perturbed Lagrangian for colliding plane electromagnetic and gravitational waves. It is shown that in both cases, there does not existComment: 18 pages, accepted for publication in Brazilian J Physic

Energy Contents of Some Well-Known Solutions in Teleparallel Gravity

In the context of teleparallel equivalent to General Relativity, we study energy and its relevant quantities for some well-known black hole solutions. For this purpose, we use the Hamiltonian approach which gives reasonable and interesting results. We find that our results of energy exactly coincide with several prescriptions in General Relativity. This supports the claim that different energy-momentum prescriptions can give identical results for a given spacetime. We also evaluate energy-momentum flux of these solutions.Comment: 16 pages, accepted for publication in Astrophys. Space Sc

Highly relativistic spinning particle in the Schwarzschild field: Circular and other orbits

The Mathisson-Papapetrou equations in the Schwarzschild background both at Mathisson-Pirani and Tulczyjew-Dixon supplementary condition are considered. The region of existence of highly relativistic circular orbits of a spinning particle in this background and dependence of the particle's orbital velocity on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle, which exist only for $r=1.5 r_g(1+\delta)$, $0<\delta \ll 1$, the corresponding orbits of a spinning particle are allowed in a wider space region, and the dimension of this region significantly depends on the supplementary condition. At the Mathisson-Pirani condition new numerical results which describe some typical cases of non-circular highly relativistic orbits of a spinning particle starting from $r>1.5 r_g$ are presented.Comment: 10 pages, 11 figure

Distribution of Energy-Momentum in a Schwarzschild-Quintessence Space-time Geometry

An analysis of the energy-momentum localization for a four-dimensional\break Schwarzschild black hole surrounded by quintessence is presented in order to provide expressions for the distributions of energy and momentum. The calculations are performed by using the Landau-Lifshitz and Weinberg energy-momentum complexes. It is shown that all the momenta vanish, while the expression for the energy depends on the mass $M$ of the black hole, the state parameter $w_{q}$ and the normalization factor $c$. The special case of $w_{q}=-2/3$ is also studied, and two limiting cases are examined.Comment: 9 page