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 $SL(2,\mathbb{C})/SO(1,1)$ 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 $\Delta = \sqrt{2}\pi = 4.44$, 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, $M \propto |\eta-\eta^*|^\beta$, we demonstrate the existence of a quantum mass gap when the classical critical exponent satisfies $\beta \geq 0.5$. When $\beta < 0.5$ 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 $\Delta u \approx 3.55$.Comment: 9 pages, revtex4, 10 ps figures; Phys. Rev. D, in pres