Order reductions of Lorentz-Dirac-like equations

We discuss the phenomenon of preacceleration in the light of a method of successive approximations used to construct the physical order reduction of a large class of singular equations. A simple but illustrative physical example is analyzed to get more insight into the convergence properties of the method.Comment: 6 pages, LaTeX, IOP macros, no figure

Exponential-Potential Scalar Field Universes I: The Bianchi I Models

We obtain a general exact solution of the Einstein field equations for the anisotropic Bianchi type I universes filled with an exponential-potential scalar field and study their dynamics. It is shown, in agreement with previous studies, that for a wide range of initial conditions the late-time behaviour of the models is that of a power-law inflating FRW universe. This property, does not hold, in contrast, when some degree of inhomogeneity is introduced, as discussed in our following paper II.Comment: 16 pages, Plain LaTeX, 1 Figure to be sent on request, to appear in Phys. Rev.

Equilibrium conditions of spinning test particles in Kerr-de Sitter spacetimes

Equilibrium conditions and spin dynamics of spinning test particles are discussed in the stationary and axially symmetric Kerr-de Sitter black-hole or naked-singularity spacetimes. The general equilibrium conditions are established, but due to their great complexity, the detailed discussion of the equilibrium conditions and spin dynamics is presented only in the simple and most relevant cases of equilibrium positions in the equatorial plane and on the symmetry axis of the spacetimes. It is shown that due to the combined effect of the rotation of the source and the cosmic repulsion the equilibrium is spin dependent in contrast to the spherically symmetric spacetimes. In the equatorial plane, it is possible at the so-called static radius, where the gravitational attraction is balanced by the cosmic repulsion, for the spinless particles as well as for spinning particles with arbitrarily large azimuthal-oriented spin or at any radius outside the ergosphere with a specifically given spin orthogonal to the equatorial plane. On the symmetry axis, the equilibrium is possible at any radius in the stationary region and is given by an appropriately tuned spin directed along the axis. At the static radii on the axis the spin of particles in equilibrium must vanish

Structural estimation of labor adjustment costs with temporally disaggregated data

Estimating labor adjustment costs is plagued by a variety of errors, many arising from data limitations. Most researchers have assumed that adjustment decisions are made at the firm level, that adjustment happens at the frequency at which a firm is observed (typically annually or quarterly), and that adjustment costs are incurred on net changes in employment. In this paper, I estimate a dynamic optimization model of labor adjustment of establishments based on data that permit 1) specifying any desired adjustment frequency, 2) estimating the model based on net and on gross employment flows and 3) allowing for simultaneous hirings and separations. The unit of observation is an establishment. Results for adjustment costs depend crucially on the model specification. Only a monthly adjustment model yields cost parameters in a reasonable range, while estimates from quarterly and annual adjustment models imply negative (adjustment implies a gain rather than a loss) or excessive adjustment costs. Estimating the model on net employment changes implies hiring and separation costs of around four annual median salaries, while the model on gross changes implies costs on the order of 1.7 annual median salaries. Adjustment costs differ significantly between small and large establishments. However, a dynamic model performs only marginally better than a static model with respect to out-of-sample predictions

Interference of outgoing electromagnetic waves generated by two point-like sources

An energy-momentum carried by electromagnetic field produced by two point-like charged particles is calculated. Integration region considered in the evaluation of the bound and emitted quantities produced by all points of world lines up to the end points at which particles' trajectories puncture an observation hyperplane $y^0=t$. Radiative part of the energy-momentum contains, apart from usual integrals of Larmor terms, also the sum of work done by Lorentz forces of point-like charges acting on one another. Therefore, the combination of wave motions (retarded Li\'enard-Wiechert solutions) leads to the interaction between the sources.Comment: 38 pages, 13 figures, LaTeX2

Dissipative cosmological solutions

The exact general solution to the Einstein equations in a homogeneous Universe with a full causal viscous fluid source for the bulk viscosity index $m=1/2$ is found. We have investigated the asymptotic stability of Friedmann and de Sitter solutions, the former is stable for $m\ge 1/2$ and the latter for $m\le 1/2$. The comparison with results of the truncated theory is made. For $m=1/2$, it was found that families of solutions with extrema no longer remain in the full case, and they are replaced by asymptotically Minkowski evolutions. These solutions are monotonic.Comment: 17 pages, LaTeX 2.09, 1 figure. To be published in Classical and Quantum Gravit

Extreme objects with arbitrary large mass, or density, and arbitrary size

We consider a generalization of the interior Schwarzschild solution that we match to the exterior one to build global C^1 models that can have arbitrary large mass, or density, with arbitrary size. This is possible because of a new insight into the problem of localizing the center of symmetry of the models and the use of principal transformations to understand the structure of space.Comment: 20 pages, 6 figures. Fixed one reference. Added a new equatio

On A Cosmological Invariant as an Observational Probe in the Early Universe

k-essence scalar field models are usually taken to have lagrangians of the form ${\mathcal L}=-V(\phi)F(X)$ with $F$ some general function of $X=\nabla_{\mu}\phi\nabla^{\mu}\phi$. Under certain conditions this lagrangian in the context of the early universe can take the form of that of an oscillator with time dependent frequency. The Ermakov invariant for a time dependent oscillator in a cosmological scenario then leads to an invariant quadratic form involving the Hubble parameter and the logarithm of the scale factor. In principle, this invariant can lead to further observational probes for the early universe. Moreover, if such an invariant can be observationally verified then the presence of dark energy will also be indirectly confirmed.Comment: 4 pages, Revte

Anisotropy and inflation in Bianchi I brane worlds

After a more general assumption on the influence of the bulk on the brane, we extend some conclusions by Maartens et al. and Santos et al. on the asymptotic behavior of Bianchi I brane worlds. As a consequence of the nonlocal anisotropic stresses induced by the bulk, in most of our models, the brane does not isotropize and the nonlocal energy does not vanish in the limit in which the mean radius goes to infinity. We have also found the intriguing possibility that the inflation due to the cosmological constant might be prevented by the interaction with the bulk. We show that the problem for the mean radius can be completely solved in our models, which include as particular cases those in the references above.Comment: 10 pages, improved discussion on the likeliness of non-isotropization, completed list of references, matches version to appear in Class. Quantum Gra

On the motion of a classical charged particle

We show that the Lorentz-Dirac equation is not an unavoidable consequence of energy-momentum conservation for a point charge. What follows solely from conservation laws is a less restrictive equation already obtained by Honig and Szamosi. The latter is not properly an equation of motion because, as it contains an extra scalar variable, it does not determine the future evolution of the charge. We show that a supplementary constitutive relation can be added so that the motion is determined and free from the troubles that are customary in Lorentz-Dirac equation, i. e. preacceleration and runaways