Analytic solutions of the geodesic equation in axially symmetric space-times

The complete sets of analytic solutions of the geodesic equation in Taub--NUT--(anti-)de Sitter, Kerr--(anti-)de Sitter and also in general Plebanski--Demianski space--times without acceleration are presented. The solutions are given in terms of the Kleinian sigma functions.Comment: 4 pages, 4 figures, accepted for publication in EP

Geodesic equations and algebro-geometric methods

For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all possible geodesic motions. Such a thorough analysis can be accomplished most effectively by using analytical methods to solve the geodesic equation. In this contribution, the use of elliptic functions and their generalizations for solving the geodesic equation in a wide range of well known space-times, which are part of the general Pleba\'nski-Demia\'nski family of solutions, will be presented. In addition, the definition and calculation of observable effects like the perihelion shift will be presented and further applications of the presented methods will be outlined.Comment: 8 pages, no figures; based on presentation at the conference "Relativity and Gravitation: 100 Years after Einstein in Prague," Prague, 2012. Relativity and Gravitation, volume 157 of Springer Proceedings in Physics, p 91. Springer International Publishing, 201

Inversion of hyperelliptic integrals of arbitrary genus with application to particle motion in General Relativity

The description of many dynamical problems like the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of a holomorphic hyperelliptic integral. The result of the inversion is defined only locally, and is done using the algebro-geometric techniques of the standard Jacobi inversion problem and the foregoing restriction to the $\theta$--divisor. For a representation of the hyperelliptic functions the Klein--Weierstra{\ss} multivariable sigma function is introduced. It is shown that all parameters needed for the calculations like period matrices and Abelian images of branch points can be expressed in terms of the periods of holomorphic differentials and theta-constants. The cases of genus two and three are considered in detail. The method is exemplified by particle motion associated with a genus three hyperelliptic curve

The Mystics of the Late Middle Ages and Their Influence on the Lutheran Reformation

Like all historical movements, the Lutheran Reformation has its antecedents in previous time. It is with one of these preparatory and influencing movements that this paper is to deal, namely, that of Late Medieval Mysticism. In this paper, we shall attempt to present the chief representatives of Late Medieval Mysticism. We have devoted three sections to each representative: first, a brief biographical sketch; secondly, an abbreviated condensation of their mysticism and theological doctrines; and thirdly, a brief evaluation of their sphere of influence and their implications for the Reformation

Health Reform, Health Insurance, and Selection: Estimating Selection into Health Insurance Using the Massachusetts Health Reform

We implement an empirical test for selection into health insurance using changes in coverage induced by the introduction of mandated health insurance in Massachusetts. Our test examines changes in the cost of the newly insured relative to those who were insured prior to the reform. We find that counties with larger increases in insurance coverage over the reform period face the smallest increase in average hospital costs for the insured population, consistent with adverse selection into insurance before the reform. Additional results, incorporating cross-state variation and data on health measures, provide further evidence for adverse selection.

Health Reform, Health Insurance, and Selection: Estimating Selection into Health Insurance Using the Massachusetts Health Reform

We implement an empirical test for selection into health insurance using changes in coverage induced by the introduction of mandated health insurance in Massachusetts. Our test examines changes in the cost of the newly insured relative to those who were insured prior to the reform. We find that counties with larger increases in insurance coverage over the reform period face the smallest increase in average hospital costs for the insured population, consistent with adverse selection into insurance before the reform. Additional results, incorporating cross-state variation and data on health measures, provide further evidence for adverse selection.Adverse selection, Massachusetts, Health reform

The complete set of solutions of the geodesic equations in the space-time of a Schwarzschild black hole pierced by a cosmic string

We study the geodesic equations in the space-time of a Schwarzschild black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of these equations for massive and massless particles, respectively. The solutions of the geodesic equations can be classified according to the particle's energy and angular momentum, the ratio between the component of the angular momentum aligned with the axis of the string and the total angular momentum, the deficit angle of the space-time and as well the horizon radius (or mass) of the black hole. For bound orbits of massive test particles we calculate the perihelion shift, we discuss light deflection and comment on the Newtonian limit.Comment: 21 pages; section 3 shortened, references added; accepted for publication in Phys. Rev.

Leading the Newly Merged High School: Exciting Opportunity or Overwhelming Challenge?

In the current economic times, school personnel are regularly challenged to reduce the costs of operating the nation’s school systems. School district consolidations often are proposed as a mechanism to realize fiscal savings for local communities; indeed, the number of U.S. school districts has declined dramatically over the past 70 years, decreasing from 117,108 in 1939-40 to 13,809 in 2008-2009