682 research outputs found
Closing the Book on the School Trust Lands
Public education in the United States faces a crisis. Financially strapped state and local governments find funding more and more difficult to supply; as a result, the quality of public education suffers. Predictably citizens are concerned, yet they resist paying increased taxes to meet the rising costs.
School trust lands provide one potential source of extra revenue. Though their existence is not well known, these lands are tremendous assets held by most states other than the original thirteen. In general, they have produced significant amounts of revenue for public education, yet historically state management of the lands has been marred by incompetence. Many of the original school trust lands have been sold or leased to private individuals for long terms at minimum values. Therefore, states have received or are receiving little return on these lands. Many states are seeking to increase revenue from the trust lands they still retain by improving management of and legislation governing school lands. In another effort to increase revenue, some states, such as Mississippi, are seeking to recover title to school lands that they have conveyed to private individuals. The Secretary of State of Mississippi has filed numerous lawsuits seeking to recover lands that were sold for inadequate consideration and also has sought to renegotiate leases that were executed for inadequate consideration.\u27 Although current attempts to recover school lands are not widespread, Mississippi has been successful, and most states that were granted school lands have the capability to file these suits and recover their lands under the existing state of the law. As state budgets continue to tighten, these lost trust lands most likely will become the subject of more litigation and more controversy. Since original school trust lands comprise over 400 million acres, many of which are economically valuable for their minerals, an upheaval in land title will create serious consequences for many individuals and private companies. The occupants of these lands are vulnerable.
This Note argues that promoting stability in land title to school trust lands is more important and economically more productive than recovering improperly sold school lands. To achieve this end, this Note suggests that the current legal framework that governs school lands, especially the adequate consideration test, should be modified. Part II outlines the source and history of the school land grants and the nature of the states\u27 trust obligations. Part III describes how these lands were sold improperly and how states now can seek to recover them by alleging either that inadequate consideration was paid for the land, or that the land was not sold according to the applicable statutory procedures. Part IV discusses and assesses legal frameworks for eliminating or limiting recovery of school lands. This Note proposes that courts limit recovery of school lands by applying statutes of limitation, estoppel, laches, or marketable record title statutes against the states. This proposal would stabilize title to school lands, but is also sympathetic to the states\u27 interests in the lands and would allow the states a limited recovery. Most importantly, the proposed framework is fair, allowing bona fide purchasers, to retain their interests in school lands
Binary black hole spacetimes with a helical Killing vector
Binary black hole spacetimes with a helical Killing vector, which are
discussed as an approximation for the early stage of a binary system, are
studied in a projection formalism. In this setting the four dimensional
Einstein equations are equivalent to a three dimensional gravitational theory
with a sigma model as the material source. The sigma
model is determined by a complex Ernst equation. 2+1 decompositions of the
3-metric are used to establish the field equations on the orbit space of the
Killing vector. The two Killing horizons of spherical topology which
characterize the black holes, the cylinder of light where the Killing vector
changes from timelike to spacelike, and infinity are singular points of the
equations. The horizon and the light cylinder are shown to be regular
singularities, i.e. the metric functions can be expanded in a formal power
series in the vicinity. The behavior of the metric at spatial infinity is
studied in terms of formal series solutions to the linearized Einstein
equations. It is shown that the spacetime is not asymptotically flat in the
strong sense to have a smooth null infinity under the assumption that the
metric tends asymptotically to the Minkowski metric. In this case the metric
functions have an oscillatory behavior in the radial coordinate in a
non-axisymmetric setting, the asymptotic multipoles are not defined. The
asymptotic behavior of the Weyl tensor near infinity shows that there is no
smooth null infinity.Comment: to be published in Phys. Rev. D, minor correction
Harrison transformation of hyperelliptic solutions and charged dust disks
We use a Harrison transformation on solutions to the stationary axisymmetric
Einstein equations to generate solutions of the Einstein-Maxwell equations. The
case of hyperelliptic solutions to the Ernst equation is studied in detail.
Analytic expressions for the metric and the multipole moments are obtained. As
an example we consider the transformation of a family of counter-rotating dust
disks. The resulting solutions can be interpreted as disks with currents and
matter with a purely azimuthal pressure or as two streams of freely moving
charged particles. We discuss interesting limiting cases as the extreme limit
where the charge becomes identical to the mass, and the ultrarelativistic limit
where the central redshift diverges.Comment: 20 pages, 9 figure
Integrable Systems in Stringy Gravity
Static axisymmetric Einstein-Maxwell-Dilaton and stationary axisymmetric
Einstein-Maxwell-Dilaton-Axion (EMDA) theories in four space-time dimensions
are shown to be integrable by means of the inverse scattering transform method.
The proof is based on the coset-space representation of the 4-dim theory in a
space-time admitting a Killing vector field. Hidden symmetry group of the
four-dimensional EMDA theory, unifying T and S string dualities, is shown to be
Sp(2, R) acting transitively on the coset Sp(2, R)/U(2). In the case of
two-parameter Abelian space-time isometry group, the hidden symmetry is the
corresponding infinite-dimensional group of the Geroch-Kinnersley-Chitre type.Comment: 8 pages, LATEX, MSU-DTP-94/21, October 9
Integrability in Theories with Local U(1) Gauge Symmetry
Using a recently developed method, based on a generalization of the zero
curvature representation of Zakharov and Shabat, we study the integrability
structure in the Abelian Higgs model. It is shown that the model contains
integrable sectors, where integrability is understood as the existence of
infinitely many conserved currents. In particular, a gauge invariant
description of the weak and strong integrable sectors is provided. The
pertinent integrability conditions are given by a U(1) generalization of the
standard strong and weak constraints for models with two dimensional target
space. The Bogomolny sector is discussed, as well, and we find that each
Bogomolny configuration supports infinitely many conserved currents. Finally,
other models with U(1) gauge symmetry are investigated.Comment: corrected typos, version accepted in J. Phys.
Continuous Self-Similarity Breaking in Critical Collapse
This paper studies near-critical evolution of the spherically symmetric
scalar field configurations close to the continuously self-similar solution.
Using analytic perturbative methods, it is shown that a generic growing
perturbation departs from the critical Roberts solution in a universal way. We
argue that in the course of its evolution, initial continuous self-similarity
of the background is broken into discrete self-similarity with echoing period
, reproducing the symmetries of the critical
Choptuik solution.Comment: RevTeX 3.1, 28 pages, 5 figures; discussion rewritten to clarify
several issue
On critical behaviour in gravitational collapse
We give an approach to studying the critical behaviour that has been observed
in numerical studies of gravitational collapse. These studies suggest, among
other things, that black holes initially form with infinitesimal mass. We show
generally how a black hole mass formula can be extracted from a transcendental
equation.
Using our approach, we give an explicit one parameter set of metrics that are
asymptotically flat and describe the collapse of apriori unspecified but
physical matter fields. The black hole mass formula obtained from this metric
exhibits a mass gap - that is, at the onset of black hole formation, the mass
is finite and non-zero.Comment: 11 pages, RevTex, 2 figures (available from VH
Properties of global monopoles with an event horizon
We investigate the properties of global monopoles with an event horizon. We
find that there is an unstable circular orbit even if a particle does not have
an angular momentum when the core mass is negative. We also obtain the
asymptotic form of solutions when the event horizon is much larger than the
core radius of the monopole, and discuss if they could be a model of galactic
halos.Comment: 5 pages, 7 figure
Quantum corrections to critical phenomena in gravitational collapse
We investigate conformally coupled quantum matter fields on spherically
symmetric, continuously self-similar backgrounds. By exploiting the symmetry
associated with the self-similarity the general structure of the renormalized
quantum stress-energy tensor can be derived. As an immediate application we
consider a combination of classical, and quantum perturbations about exactly
critical collapse. Generalizing the standard argument which explains the
scaling law for black hole mass, , we
demonstrate the existence of a quantum mass gap when the classical critical
exponent satisfies . When our argument is
inconclusive; the semi-classical approximation breaks down in the spacetime
region of interest.Comment: RevTeX, 6 pages, 3 figures included using psfi
Galerkin Method in the Gravitational Collapse: a Dynamical System Approach
We study the general dynamics of the spherically symmetric gravitational
collapse of a massless scalar field. We apply the Galerkin projection method to
transform a system of partial differential equations into a set of ordinary
differential equations for modal coefficients, after a convenient truncation
procedure, largely applied to problems of turbulence. In the present case, we
have generated a finite dynamical system that reproduces the essential features
of the dynamics of the gravitational collapse, even for a lower order of
truncation. Each initial condition in the space of modal coefficients
corresponds to a well definite spatial distribution of scalar field. Numerical
experiments with the dynamical system show that depending on the strength of
the scalar field packet, the formation of black-holes or the dispersion of the
scalar field leaving behind flat spacetime are the two main outcomes. We also
found numerical evidence that between both asymptotic states, there is a
critical solution represented by a limit cycle in the modal space with period
.Comment: 9 pages, revtex4, 10 ps figures; Phys. Rev. D, in pres
- âŠ