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

Cancer mortality in the United Kingdom: projections to the year 2025

The purpose of this study was to project mortality rates in the United Kingdom for the period 2006–2025 for 21 major cancers on the basis of the observed trends in mortality rates during 1971–2005, and to estimate the implication in terms of expected deaths. Age-period-cohort models were applied to official statistics. The projected decrease in age-standardised mortality rates for all cancers from 2003 to 2023 was 17% in men and 16% in women. Future mortality rates were projected to decline for most cancer sites. In men, there were small projected increases in mortality rates from cancers of the oral cavity, oesophagus and melanoma, with a larger projected increase (14% over 20 years) in mortality of liver cancer. In women, the only projected increase (18%) was for corpus uteri. The numbers of deaths will increase for most cancers, with a 30% increase in all cancers projected for men and a 12% increase projected for women. Mortality rates from cancer as a whole have been falling in the United Kingdom since 1990, and this decline was projected to continue into the future as well as the declining rates in both sexes for most cancers. Actual numbers of deaths will increase for most cancers

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

Teleparallel Killing Vectors of Spherically Symmetric Spacetimes

In this paper, Killing vectors of spherically spacetimes have been evaluated in the context of teleparallel theory of gravitation. Further, we investigate the Killing vectors of the Friedmann metrics. It is found that for static spherically spacetimes the number of Killing vectors turn out to be \emph{seven} while for the Friedmann models, we obtain \emph{six} teleparallel Killing vectors. The results are then compared with those of General Relativity. We conclude that both of these descriptions of gravity do not provide the consistent results in general. However, these results may coincide under certain conditions for a particular spacetime.Comment: 14 pages, accepted for publication in Communications in Theoretical Physic

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

An analytical treatment of the Clock Paradox in the framework of the Special and General Theories of Relativity

In this paper we treat the so called clock paradox in an analytical way by assuming that a constant and uniform force F of finite magnitude acts continuously on the moving clock along the direction of its motion assumed to be rectilinear. No inertial motion steps are considered. The rest clock is denoted as (1), the to-and-fro moving clock is (2), the inertial frame in which (1) is at rest in its origin and (2) is seen moving is I and, finally, the accelerated frame in which (2) is at rest in its origin and (1) moves forward and backward is A. We deal with the following questions: I) What is the effect of the finite force acting on (2) on the proper time intervals measured by the two clocks when they reunite? Does a differential aging between the two clocks occur, as it happens when inertial motion and infinite values of the accelerating force is considered? The Special Theory of Relativity is used in order to describe the hyperbolic motion of (2) in the frame I II) Is this effect an absolute one, i.e. does the accelerated observer A comoving with (2) obtain the same results as that in I, both qualitatively and quantitatively, as it is expected? We use the General Theory of Relativity in order to answer this question.Comment: LaTex2e, 19 pages, no tables, no figures. Rewritten version, it amends the previous one whose results about the treatment with General Relativity were wrong. References added. Eq. (55) corrected. More refined version. Comments and suggestions are warmly welcom

Conservation laws for vacuum tetrad gravity

Ten conservation laws in useful polynomial form are derived from a Cartan form and Exterior Differential System (EDS) for the tetrad equations of vacuum relativity. The Noether construction of conservation laws for well posed EDS is introduced first, and an illustration given, deriving 15 conservation laws of the free field Maxwell Equations from symmetries of its EDS. The Maxwell EDS and tetrad gravity EDS have parallel structures, with their numbers of dependent variables, numbers of generating 2-forms and generating 3-forms, and Cartan character tables all in the ratio of 1 to 4. They have 10 corresponding symmetries with the same Lorentz algebra, and 10 corresponding conservation laws.Comment: Final version with additional reference

Locality hypothesis and the speed of light

The locality hypothesis is generally considered necessary for the study of the kinematics of non-inertial systems in special relativity. In this paper we discuss this hypothesis, showing the necessity of an improvement, in order to get a more clear understanding of the various concepts involved, like coordinate velocity and standard velocity of light. Concrete examples are shown, where these concepts are discussed.Comment: 23 page

Currents and Superpotentials in classical gauge theories: II. Global aspects and the example of Affine gravity

The conserved charges associated to gauge symmetries are defined at a boundary component of space-time because the corresponding Noether current can be rewritten on-shell as the divergence of a superpotential. However, the latter is afflicted by ambiguities. Regge and Teitelboim found a procedure to lift the arbitrariness in the Hamiltonian framework. An alternative covariant formula was proposed by one of us for an arbitrary variation of the superpotential, it depends only on the equations of motion and on the gauge symmetry under consideration. Here we emphasize that in order to compute the charges, it is enough to stay at a boundary of spacetime, without requiring any hypothesis about the bulk or about other boundary components, so one may speak of holographic charges. It is well known that the asymptotic symmetries that lead to conserved charges are really defined at infinity, but the choice of boundary conditions and surface terms in the action and in the charges is usually determined through integration by parts whereas each component of the boundary should be considered separately. We treat the example of gravity (for any space-time dimension, with or without cosmological constant), formulated as an Affine theory which is a natural generalization of the Palatini and Cartan-Weyl (vielbein) first order formulations. We then show that the superpotential associated to a Dirichlet boundary condition on the metric (the one needed to treat asymptotically flat or AdS spacetimes) is the one proposed by Katz, Bi\u{c}{\'a}k and Lynden-Bell and not that of Komar. We finally discuss the KBL superpotential at null infinity.Comment: 16 pages, minor corrections and references added. Final version to appear in CQ

The gravitational energy-momentum flux

We present a continuity equation for the gravitational energy-momentum, which is obtained in the framework of the teleparallel equivalent of general relativity. From this equation it follows a general definition for the gravitational energy-momentum flux. This definition is investigated in the context of plane waves and of cylindrical Einstein-Rosen waves. We obtain the well known value for the energy flux of plane gravitational waves, and conclude that the latter exhibit features similar to plane electromagnetic waves.Comment: 20 pages, latex file, no figures, two references added, accepted for publication in Class. Quantum Gravit