Matter and dynamics in closed cosmologies

To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general barotropic equation of state can be treated. We focus on locally rotationally symmetric Bianchi type IX and Kantowski-Sachs orthogonal perfect fluid models, since such models exhibit a particularly rich dynamical structure and also illustrate typical features of more general cases. For these models, we recast Einstein's field equations into a regular system on a compact state space, which is the basis for our analysis. We prove that models expand from a singularity and recollapse to a singularity when the perfect fluid satisfies the strong energy condition. When the matter source admits Einstein's static model, we present a comprehensive dynamical description, which includes asymptotic behavior, of models in the neighborhood of the Einstein model; these results make earlier claims about ``homoclinic phenomena and chaos'' highly questionable. We also discuss aspects of the global asymptotic dynamics, in particular, we give criteria for the collapse to a singularity, and we describe when models expand forever to a state of infinite dilution; possible initial and final states are analyzed. Numerical investigations complement the analytical results.Comment: 23 pages, 24 figures (compressed), LaTe

Radio Emission and Particle Acceleration in SN 1993J

The radio light curves of SN 1993J are found to be well fit by a synchrotron spectrum, suppressed by external free-free absorption and synchrotron self-absorption. A standard r^-2 circumstellar medium is assumed, and found to be adequate. The magnetic field and number density of relativistic electrons behind the shock are determined. The strength of the magnetic field argues strongly for turbulent amplification behind the shock. The ratio of the magnetic and thermal energy density behind the shock is ~0.14. Synchrotron and Coulomb cooling dominate the losses of the electrons. The injected electron spectrum has a power law index -2.1, consistent with diffusive shock acceleration, and the number density scales with the thermal electron energy density. The total energy density of the relativistic electrons is, if extrapolated to gamma ~ 1, ~ 5x10^-4 of the thermal energy density. The free-free absorption required is consistent with previous calculations of the circumstellar temperature of SN 1993J, T_e ~ (2-10)x10^5 K. The relative importance of free-free absorption, Razin suppression, and the synchrotron self-absorption effect for other supernovae are briefly discussed. Guidelines for the modeling and interpretation of VLBI observations are given.Comment: accepted for Ap.

Asymptotic silence of generic cosmological singularities

In this letter we investigate the nature of generic cosmological singularities using the framework developed by Uggla et al. We do so by studying the past asymptotic dynamics of general vacuum G2 cosmologies, models that are expected to capture the singular behavior of generic cosmologies with no symmetries at all. In particular, our results indicate that asymptotic silence holds, i.e., that particle horizons along all timelines shrink to zero for generic solutions. Moreover, we provide evidence that spatial derivatives become dynamically insignificant along generic timelines, and that the evolution into the past along such timelines is governed by an asymptotic dynamical system which is associated with an invariant set -- the silent boundary. We also identify an attracting subset on the silent boundary that organizes the oscillatory dynamics of generic timelines in the singular regime. In addition, we discuss the dynamics associated with recurring spike formation.Comment: 4 pages, 5 *.eps figures, RevTeX4; replaced by significantly revised version, to appear in Physical Review Letter

Homoclinic chaos and energy condition violation

In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where the matter is assumed to be non-tilted dust and a positive cosmological constant. We show that homoclinic chaos in these models is an artifact of unphysical assumptions: it requires that there exist solutions with positive matter energy density $\rho>0$ that evolve through the singularity and beyond as solutions with negative matter energy density $\rho<0$. Homoclinic chaos is absent when it is assumed that the dust particles always retain their positive mass.In addition, we discuss more general models: for solutions that are not locally rotionally symmetric we demonstrate that the construction of extensions through the singularity, which is required for homoclinic chaos, is not possible in general.Comment: 4 pages, RevTe

Using the Uncharged Kerr Black Hole as a Gravitational Mirror

We extend the study of the possibility to use the Schwarzschild black hole as a gravitational mirror to the more general case of an uncharged Kerr black hole. We use the null geodesic equation in the equatorial plane to prove a theorem concerning the conditions the impact parameter has to satisfy if there shall exist boomerang photons. We derive an equation for these boomerang photons and an equation for the emission angle. Finally, the radial null geodesic equation is integrated numerically in order to illustrate boomerang photons.Comment: 11 pages Latex, 3 Postscript figures, uufiles to compres

How Does Customer Service Offshoring Impact Customer Satisfaction?

Information technology (IT) plays a vital role in customer relationship management (CRM), because CRM processes include the collection and analysis of customer information, firms use technology tools to interact with customers, and IT created the conditions under which firms can offshore CRM processes. Customers have negative perceptions toward offshoring, which suggests that firms might be reluctant to offshore IT-enabled CRM processes. However, firms have significantly increased offshoring for CRM processes, presenting a conundrum. Why would firms increase offshoring for CRM processes if there could be a risk to customer satisfaction? This paper helps to resolve the conundrum by studying the impact of CRM sourcing on customer satisfaction with the firm’s products and services, as measured by the American Customer Satisfaction IndexTM. We analyze data for 150 North American firms and business units over a nine-year period. Front office offshore outsourcing and front office onshore outsourcing are both negatively associated with customer satisfaction, which suggests that negative customer perceptions may be due to the firm boundary dimension rather than the geographic location dimension. Front office offshore outsourcing is not statistically significant for services firms, which suggests that customers are more accepting of offshore providers in a service setting. Over time, the coefficient for back office offshore outsourcing has become more positive, which suggests that firms may expect to see a similar improvement for front office offshore outsourcing in the future. Our empirical results provide a basis to understand why firms have increased IT-enabled CRM offshoring despite short-term risks to customer satisfaction