World-line deviation and spinning particles

A set of world-line deviation equations is derived in the framework of Mathisson-Papapetrou-Dixon description of pseudo-classical spinning particles. They generalize the geodesic deviation equations. We examine the resulting equations for particles moving in the space-time of a plane gravitational wave.Comment: 5 pages, no figures, to appear in Physics Letters

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

Lagrangian description of world-line deviations

We introduce a Lagrangian which can be varied to give both the equation of motion and world-line deviations of spinning particles simultaneously.Comment: to appear in IJT

On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories

We generalize the notion of quasi-local charges, introduced by P. Tod for Yang--Mills fields with unitary groups, to non-Abelian gauge theories with arbitrary gauge group, and calculate its small sphere and large sphere limits both at spatial and null infinity. We show that for semisimple gauge groups no reasonable definition yield conserved total charges and Newman--Penrose (NP) type quantities at null infinity in generic, radiative configurations. The conditions of their conservation, both in terms of the field configurations and the structure of the gauge group, are clarified. We also calculate the NP quantities for stationary, asymptotic solutions of the field equations with vanishing magnetic charges, and illustrate these by explicit solutions with various gauge groups.Comment: 22 pages, typos corrected, appearing in Classical and Quantum Gravit

Path and Path Deviation Equations for p-branes

Path and path deviation equations for neutral, charged, spinning and spinning charged test particles, using a modified Bazanski Lagrangian, are derived. We extend this approach to strings and branes. We show how the Bazanski Lagrangian for charged point particles and charged branes arises `a la Kaluza-Klein from the Bazanski Lagrangian in 5-dimensions.Comment: 13 pages, LaTeX fil

The Generalized Jacobi Equation

The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighboring but their relative velocity is arbitrary the corresponding geodesic deviation equation is the generalized Jacobi equation. The Hamiltonian structure of this nonlinear equation is analyzed in this paper. The tidal accelerations for test particles in the field of a plane gravitational wave and the exterior field of a rotating mass are investigated. In the latter case, the existence of an attractor of uniform relative radial motion with speed $2^{-1/2}c\approx 0.7 c$ is pointed out. The astrophysical implications of this result for the terminal speed of a relativistic jet is briefly explored.Comment: LaTeX file, 4 PS figures, 28 pages, revised version, accepted for publication in Classical and Quantum Gravit

Effectiveness of Adaptive Silverware on Range of Motion of the Hand

Background: Hand function is essential to a person’s self-efficacy and greatly affects quality of life. Adapted utensils with handles of increased diameters have historically been used to assist individuals with arthritis or other hand disabilities for feeding, and other related activities of daily living. To date, minimal research has examined the biomechanical effects of modified handles, or quantified the differences in ranges of motion (ROM) when using a standard versus a modified handle. The aim of this study was to quantify the ranges of motion (ROM) required for a healthy hand to use different adaptive spoons with electrogoniometry for the purpose of understanding the physiologic advantages that adapted spoons may provide patients with limited ROM. Methods: Hand measurements included the distal interphalangeal joint (DIP), proximal interphalangeal joint (PIP), and metacarpophalangeal joint (MCP) for each finger and the interphalangeal (IP) and MCP joint for the thumb. Participants were 34 females age 18-30 (mean age 20.38 ± 1.67) with no previous hand injuries or abnormalities. Participants grasped spoons with standard handles, and spoons with handle diameters of 3.18 cm (1.25 inch), and 4.45 cm (1.75 inch). ROM measurements were obtained with an electrogoniometer to record the angle at each joint for each of the spoon handle sizes. Results: A 3 x 3 x 4 repeated measures ANOVA (Spoon handle size by Joint by Finger) found main effects on ROM of Joint (F (2,33) = 318.68, Partial η2= .95, p < .001), Spoon handle size (F (2,33) = 598.73, Partial η2 = .97, p < .001), and Finger (F (3,32) = 163.83, Partial η2 = .94, p < .001). As the spoon handle diameter size increased, the range of motion utilized to grasp the spoon handle decreased in all joints and all fingers (P < 0.01). Discussion: This study confirms the hypothesis that less range of motion is required to grip utensils with larger diameter handles, which in turn may reduce challenges for patients with limited ROM of the hand

Components of the gravitational force in the field of a gravitational wave

Gravitational waves bring about the relative motion of free test masses. The detailed knowledge of this motion is important conceptually and practically, because the mirrors of laser interferometric detectors of gravitational waves are essentially free test masses. There exists an analogy between the motion of free masses in the field of a gravitational wave and the motion of free charges in the field of an electromagnetic wave. In particular, a gravitational wave drives the masses in the plane of the wave-front and also, to a smaller extent, back and forth in the direction of the wave's propagation. To describe this motion, we introduce the notion of `electric' and `magnetic' components of the gravitational force. This analogy is not perfect, but it reflects some important features of the phenomenon. Using different methods, we demonstrate the presence and importance of what we call the `magnetic' component of motion of free masses. It contributes to the variation of distance between a pair of particles. We explicitely derive the full response function of a 2-arm laser interferometer to a gravitational wave of arbitrary polarization. We give a convenient description of the response function in terms of the spin-weighted spherical harmonics. We show that the previously ignored `magnetic' component may provide a correction of up to 10 %, or so, to the usual `electric' component of the response function. The `magnetic' contribution must be taken into account in the data analysis, if the parameters of the radiating system are not to be mis-estimated.Comment: prints to 29 pages including 9 figures, new title, additional explanations and references in response to referee's comments, to be published in Class. Quant. Gra

Enthalpy and the Mechanics of AdS Black Holes

We present geometric derivations of the Smarr formula for static AdS black holes and an expanded first law that includes variations in the cosmological constant. These two results are further related by a scaling argument based on Euler's theorem. The key new ingredient in the constructions is a two-form potential for the static Killing field. Surface integrals of the Killing potential determine the coefficient of the variation of the cosmological constant in the first law. This coefficient is proportional to a finite, effective volume for the region outside the AdS black hole horizon, which can also be interpreted as minus the volume excluded from a spatial slice by the black hole horizon. This effective volume also contributes to the Smarr formula. Since the cosmological constant is naturally thought of as a pressure, the new term in the first law has the form of effective volume times change in pressure that arises in the variation of the enthalpy in classical thermodynamics. This and related arguments suggest that the mass of an AdS black hole should be interpreted as the enthalpy of the spacetime.Comment: 21 pages; v2 references adde