About Gravitomagnetism

The gravitomagnetic field is the force exerted by a moving body on the basis of the intriguing interplay between geometry and dynamics which is the analog to the magnetic field of a moving charged body in electromagnetism. The existence of such a field has been demonstrated based on special relativity approach and also by special relativity plus the gravitational time dilation for two different cases, a moving infinite line and a uniformly moving point mass, respectively. We treat these two approaches when the applied cases are switched while appropriate key points are employed. Thus, we demonstrate that the strength of the resulted gravitomagnetic field in the latter approach is twice the former. Then, we also discuss the full linearized general relativity and show that it should give the same strength for gravitomagnetic field as the latter approach. Hence, through an exact analogy with the electrodynamic equations, we present an argument in order to indicate the best definition amongst those considered in this issue in the literature. Finally, we investigate the gravitomagnetic effects and consequences of different definitions on the geodesic equation including the second order approximation terms.Comment: 16 pages, a few amendments have been performed and a new section has been adde

Classical Trace Anomaly

We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy-momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation should perhaps be, classically, somehow related to the covariance of the form of Einstein's equations.Comment: Version 2: 21 pages, TeX file (using phyzzx.tex), added new section and references. Version 3: Just replaced Abstrac

Quantum mechanics and geodesic deviation in the brane world

We investigate the induced geodesic deviation equations in the brane world models, in which all the matter forces except gravity are confined on the 3-brane. Also, the Newtonian limit of induced geodesic deviation equation is studied. We show that in the first Randall-Sundrum model the Bohr-Sommerfeld quantization rule is as a result of consistency between the geodesic and geodesic deviation equations. This indicates that the path of test particle is made up of integral multiples of a fundamental Compton-type unit of length $h/mc$.Comment: 5 pages, no figure

Black holes in the varying speed of light theory

We consider the effect of the \emph{Varying Speed of Light} theory on non-rotating black holes. We show that in any varying-$c$ theory, the Schwarzschild solution is neither static nor stationary. For a no-charged black hole, the singularity in the Schwarzschild horizon cannot be removed by coordinate transformation. Hence, no matter can enter the horizon, and the interior part of the black hole is separated from the rest of the Universe. If $\dot{c}<0$, then the size of the Schwarzschild radius increases with time. The higher value of the speed of light in the very early Universe may have caused a large reduction in the probability of the creation of the primordial black holes and their population.The same analogy is also considered for the charged black holes.Comment: 5 page

An analytical calculation of frictional and bending moments at the head-neck interface of hip joint implants during different physiological activities

This study predicts the frictional moments at the head-cup interface and frictional torques and bending moments acting on the head-neck interface of a modular total hip replacement across a range of activities of daily living. The predicted moment and torque profiles are based on the kinematics of four patients and the implant characteristics of a metal-on-metal implant. Depending on the body weight and type of activity, the moments and torques had significant variations in both magnitude and direction over the activity cycles. For the nine investigated activities, the maximum magnitude of the frictional moment ranged from 2.6 to 7.1 Nm. The maximum magnitude of the torque acting on the head-neck interface ranged from 2.3 to 5.7 Nm. The bending moment acting on the head-neck interface varied from 7 to 21.6 Nm. One-leg-standing had the widest range of frictional torque on the head-neck interface (11 Nm) while normal walking had the smallest range (6.1 Nm). The widest range, together with the maximum magnitude of torque, bending moment, and frictional moment, occurred during one-leg-standing of the lightest patient. Most of the simulated activities resulted in frictional torques that were near the previously reported oxide layer depassivation threshold torque. The predicted bending moments were also found at a level believed to contribute to the oxide layer depassivation. The calculated magnitudes and directions of the moments, applied directly to the head-neck taper junction, provide realistic mechanical loading data for in vitro and computational studies on the mechanical behaviour and multi-axial fretting at the head-neck interface.Hamidreza Farhoudi, Reza H. Oskouei, Ali A. Pasha Zanoosi, Claire F. Jones and Mark Taylo