Covariant Uniform Acceleration

We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. We compute explicit solutions for uniformly accelerated motion which are divided into four types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. We obtain an interpretation of the Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.Comment: 36 page

Revising the multipole moments of numerical spacetimes, and its consequences

Identifying the relativistic multipole moments of a spacetime of an astrophysical object that has been constructed numerically is of major interest, both because the multipole moments are intimately related to the internal structure of the object, and because the construction of a suitable analytic metric that mimics a numerical metric should be based on the multipole moments of the latter one, in order to yield a reliable representation. In this note we show that there has been a widespread delusion in the way the multipole moments of a numerical metric are read from the asymptotic expansion of the metric functions. We show how one should read correctly the first few multipole moments (starting from the quadrupole mass-moment), and how these corrected moments improve the efficiency of describing the metric functions with analytic metrics that have already been used in the literature, as well as other consequences of using the correct moments.Comment: article + supplemental materia

Quasi-Chemical and Structural Analysis of Polarizable Anion Hydration

Quasi-chemical theory is utilized to analyze the roles of solute polarization and size in determining the structure and thermodynamics of bulk anion hydration for the Hofmeister series Cl$^-$, Br$^-$, and I$^-$. Excellent agreement with experiment is obtained for whole salt hydration free energies using the polarizable AMOEBA force field. The quasi-chemical approach exactly partitions the solvation free energy into inner-shell, outer-shell packing, and outer-shell long-ranged contributions by means of a hard-sphere condition. Small conditioning radii, even well inside the first maximum of the ion-water(oxygen) radial distribution function, result in Gaussian behavior for the long-ranged contribution that dominates the ion hydration free energy. The spatial partitioning allows for a mean-field treatment of the long-ranged contribution, leading to a natural division into first-order electrostatic, induction, and van der Waals terms. The induction piece exhibits the strongest ion polarizability dependence, while the larger-magnitude first-order electrostatic piece yields an opposing but weaker polarizability dependence. In addition, a structural analysis is performed to examine the solvation anisotropy around the anions. As opposed to the hydration free energies, the solvation anisotropy depends more on ion polarizability than on ion size: increased polarizability leads to increased anisotropy. The water dipole moments near the ion are similar in magnitude to bulk water, while the ion dipole moments are found to be significantly larger than those observed in quantum mechanical studies. Possible impacts of the observed over-polarization of the ions on simulated anion surface segregation are discussed.Comment: slight revision, in press at J. Chem. Phy

Testing Einstein's time dilation under acceleration using M\"ossbauer spectroscopy

The Einstein time dilation formula was tested in several experiments. Many trials have been made to measure the transverse second order Doppler shift by M\"{o}ssbauer spectroscopy using a rotating absorber, to test the validity of this formula. Such experiments are also able to test if the time dilation depends only on the velocity of the absorber, as assumed by Einstein's clock hypothesis, or the present centripetal acceleration contributes to the time dilation. We show here that the fact that the experiment requires $\gamma$-ray emission and detection slits of finite size, the absorption line is broadened; by geometric longitudinal first order Doppler shifts immensely. Moreover, the absorption line is non-Lorenzian. We obtain an explicit expression for the absorption line for any angular velocity of the absorber. The analysis of the experimental results, in all previous experiments which did not observe the full absorption line itself, were wrong and the conclusions doubtful. The only proper experiment was done by K\"{u}ndig (Phys. Rev. 129 (1963) 2371), who observed the broadening, but associated it to random vibrations of the absorber. We establish necessary conditions for the successful measurement of a transverse second order Doppler shift by M\"{o}ssbauer spectroscopy. We indicate how the results of such an experiment can be used to verify the existence of a Doppler shift due to acceleration and to test the validity of Einstein's clock hypothesis.Comment: 11 pages, 4 figure

Realistic calculations of nuclear disappearance lifetimes induced by neutron-antineutron oscillations

Realistic calculations of nuclear disappearance lifetimes induced by neutron-antineutron oscillations are reported for oxygen and iron, using antineutron nuclear potentials derived from a recent comprehensive analysis of antiproton atomic X-ray and radiochemical data. A lower limit of 3.3 x 10E8 s on the neutron-antineutron oscillation time is derived from the Super-Kamiokande I new lower limit of 1.77 x 10E32 yr on the neutron lifetime in oxygen. Antineutron scattering lengths in carbon and nickel, needed in trap experiments using ultracold neutrons, are calculated from updated antinucleon optical potentials at threshold, with results shown to be largely model independent.Comment: version matching PRD publication, typos and references correcte

An airborne remote sensing system for urban air quality

Several NASA sponsored remote sensors and possible airborne platforms were evaluated. Outputs of dispersion models for SO2 and CO pollution in the Washington, D.C. area were used with ground station data to establish the expected performance and limitations of the remote sensors. Aircraft/sensor support requirements are discussed. A method of optimum flight plan determination was made. Cost trade offs were performed. Conclusions about the implementation of various instrument packages as parts of a comprehensive air quality monitoring system in Washington are presented

Nuclear Multifragmentation Critical Exponents

We show that the critical exponents of nuclear multi-fragmentation have not been determined conclusively yet.Comment: 3 pages, LaTeX, one postscript figure appended, sub. to Phys.Rev.Lett. as a commen

Anomalous Hall Effect in Ferromagnetic Semiconductors in the Hopping Transport Regime

We present a theory of the Anomalous Hall Effect (AHE) in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity $\sigma_{xy}^{AH}$. We show that $\sigma_{xy}^{AH}$ is proportional to the first derivative of the density of states $\varrho(\epsilon)$ and thus can be expected to change sign as a function of impurity band filling. We also show that $\sigma_{xy}^{AH}$ depends on temperature as the longitudinal conductivity $\sigma_{xx}$ within logarithmic accuracy.Comment: 4 pages, 1 eps figure, final versio

Organizing to Win: Introduction

[Excerpt] The American labor movement is at a watershed. For the first time since the early years of industrial unionism sixty years ago, there is near-universal agreement among union leaders that the future of the movement depends on massive new organizing. In October 1995, John Sweeney, Richard Trumka, and Linda Chavez-Thompson were swept into the top offices of the AFL-CIO, following a campaign that promised organizing at an unprecedented pace and scale. Since taking office, the new AFL-CIO leadership team has created a separate organizing department and has committed $20 million to support coordinated large-scale industry-based organizing drives. In addition, in the summer of 1996, the AFL-CIO launched the Union Summer program, which placed more than a thousand college students and young workers in organizing campaigns across the country

The rotational modes of relativistic stars: Numerical results

We study the inertial modes of slowly rotating, fully relativistic compact stars. The equations that govern perturbations of both barotropic and non-barotropic models are discussed, but we present numerical results only for the barotropic case. For barotropic stars all inertial modes are a hybrid mixture of axial and polar perturbations. We use a spectral method to solve for such modes of various polytropic models. Our main attention is on modes that can be driven unstable by the emission of gravitational waves. Hence, we calculate the gravitational-wave growth timescale for these unstable modes and compare the results to previous estimates obtained in Newtonian gravity (i.e. using post-Newtonian radiation formulas). We find that the inertial modes are slightly stabilized by relativistic effects, but that previous conclusions concerning eg. the unstable r-modes remain essentially unaltered when the problem is studied in full general relativity.Comment: RevTeX, 29 pages, 31 eps figure