Action functionals of single scalar fields and arbitrary--weight gravitational constraints that generate a genuine Lie algebra

We discuss the issue initiated by Kucha\v{r} {\it et al}, of replacing the usual Hamiltonian constraint by alternative combinations of the gravitational constraints (scalar densities of arbitrary weight), whose Poisson brackets strongly vanish and cast the standard constraint-system for vacuum gravity into a form that generates a true Lie algebra. It is shown that any such combination---that satisfies certain reality conditions---may be derived from an action principle involving a single scalar field and a single Lagrange multiplier with a non--derivative coupling to gravity.Comment: 26 pages, plain TE

Quasi-exactly solvable quartic potential

A new two-parameter family of quasi-exactly solvable quartic polynomial potentials $V(x)=-x^4+2iax^3+(a^2-2b)x^2+2i(ab-J)x$ is introduced. Until now, it was believed that the lowest-degree one-dimensional quasi-exactly solvable polynomial potential is sextic. This belief is based on the assumption that the Hamiltonian must be Hermitian. However, it has recently been discovered that there are huge classes of non-Hermitian, ${\cal PT}$-symmetric Hamiltonians whose spectra are real, discrete, and bounded below [physics/9712001]. Replacing Hermiticity by the weaker condition of ${\cal PT}$ symmetry allows for new kinds of quasi-exactly solvable theories. The spectra of this family of quartic potentials discussed here are also real, discrete, and bounded below, and the quasi-exact portion of the spectra consists of the lowest $J$ eigenvalues. These eigenvalues are the roots of a $J$th-degree polynomial.Comment: 3 Pages, RevTex, 1 Figure, encapsulated postscrip

Radiative damping: a case study

We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B. This is a physically relevant, but difficult dynamical problem, to which contributions range over more than one hundred years. Specifically, we will study the Sommerfeld-Page approximation which assumes an extended charge distribution at small velocities. The memory equation is then linear and many details become available. We discuss how the friction equation arises in the limit of "small" B and contrast this result with the standard Taylor expansion resulting in a second order equation for the velocity of the charge.Comment: 4 figure

Statistical Mechanics of Three-dimensional Kerr-de Sitter Space

The statistical computation of the (2+1)-dimensional Kerr-de Sitter space in the context of the {\it classical} Virasoro algebra for an asymptotic isometry group has been a mystery since first, the degeneracy of the states has the right value only at the infinite boundary which is casually disconnected from our universe, second, the analyses were based on the unproven Cardy's formula for complex central charge and conformal weight. In this paper, I consider the entropy in Carlip's "would-be gauge" degrees of freedom approach instead. I find that it agree with the Bekenstein-Hawking entropy but there are no the above problems. Implications to the dS/CFT are noted.Comment: Added comments about diffeomorphism generators and Wheeler-de Witt equation; Added references; Accpected in CQ

Mass-Radius Relation for Magnetic White Dwarfs

Recently, several white dwarfs with very strong surface magnetic fields have been observed. In this paper we explore the possibility that such stars could have sufficiently strong internal fields to alter their structure. We obtain a revised white dwarf mass-radius relation in the presence of strong internal magnetic fields. We first derive the equation of state for a fully degenerate ideal electron gas in a magnetic field using an Euler-MacLaurin expansion. We use this to obtain the mass-radius relation for magnetic $^{4}$He, $^{12}$C, and $^{56}$Fe white dwarfs of uniform composition.Comment: 7 pages, 7 figures and 1 table, To appear in Ap

Inhomogeneous ground state and the coexistence of two length scales near phase transitions in real solids

Real crystals almost unavoidably contain a finite density of dislocations. We show that this generic type of long--range correlated disorder leads to a breakdown of the conventional scenario of critical behavior and standard renormalization group techniques based on the existence of a simple, homogeneous ground state. This breakdown is due to the appearance of an inhomogeneous ground state that changes the character of the phase transition to that of a percolative phenomenon. This scenario leads to a natural explanation for the appearance of two length scales in recent high resolution small-angle scattering experiments near magnetic and structural phase transitions.Comment: 4 pages, RevTex, no figures; also available from http://www.tp3.ruhr-uni-bochum.de/archive/tpiii_archive.htm

Cold ideal equation of state for strongly magnetized neutron-star matter: effects on muon production and pion condensationn

Neutron stars with very strong surface magnetic fields have been suggested as the site for the origin of observed soft gamma repeaters (SGRs). In this paper we investigate the influence of such strong magnetic fields on the properties and internal structure of these magnetized neutron stars (magnetars). We study properties of a degenerate equilibrium ideal neutron-proton-electron (npe) gas with and without the effects of the anomalous nucleon magnetic moments in a magnetic field. The presence of a sufficiently strong magnetic field changes the ratio of protons to neutrons as well as the neutron drip density. We also study the appearance of muons as well as pion condensation in strong magnetic fields. We discuss the possibility that boson condensation in the interior of magnetars might be a source of SGRs.Comment: 10 pages included 9 figures, ApJ in pres

Lack of Mutual Respect in Relationship The Endangered Partner

Violence in a relationship and in a family setting has been an issue of concern to various interest groups and professional organizations. Of particular interest in this article is violence against women in a relationship. While there is an abundance of knowledge on violence against women in general, intimate or partner femicide seems to have received less attention. Unfortunately, the incidence of violence against women, and intimate femicide in particular, has been an issue of concern in the African setting. This article examines the trends of intimate femicide in an African setting in general, and in Botswana in particular. The increase in intimate femicide is an issue of concern, which calls for collective effort to address. This article also examines trends offemicide in Botswana, and the antecedents and the precipitating factors. Some studies have implicated societal and cultural dynamics as playing significant roles in intimate femicide in the African setting. It is believed that the patriarchal nature of most African settings and the ideology of male supremacy have relegated women to a subordinate role. Consequently, respect for women in any relationship with men is lopsided in favor of men and has led to abuse of women, including intimate femicide. Other militating factors in intimate femicide ,are examined and the implications for counseling to assist the endangered female partner are discussed