High gradient directional solidification furnace

A high gradient directional solidification furnace is disclosed which includes eight thermal zones throughout the length of the furnace. In the hot end of the furnace, furnace elements provide desired temperatures. These elements include Nichrome wire received in a grooved tube which is encapsulated y an outer alumina core. A booster heater is provided in the hot end of the furnace which includes toroidal tungsten/rhenium wire which has a capacity to put heat quickly into the furnace. An adiabatic zone is provided by an insulation barrier to separate the hot end of the furnace from the cold end. The old end of the furnace is defined by additional heating elements. A heat transfer plate provides a means by which heat may be extracted from the furnace and conducted away through liquid cooled jackets. By varying the input of heat via the booster heater and output of heat via the heat transfer plate, a desired thermal gradient profile may be provided

General purpose rocket furnace

A multipurpose furnace for space vehicles used for material processing experiments in an outer space environment is described. The furnace contains three separate cavities designed to process samples of the widest possible range of materials and thermal requirements. Each cavity contains three heating elements capable of independent function under the direction of an automatic and programmable control system. A heat removable mechanism is also provided for each cavity which operates in conjunction with the control system for establishing an isothermally heated cavity or a wide range of thermal gradients and cool down rates. A monitoring system compatible with the rocket telemetry provides furnace performance and sample growth rate data throughout the processing cycle

Dirty black holes: Entropy versus area

Considerable interest has recently been expressed in the entropy versus area relationship for ``dirty'' black holes --- black holes in interaction with various classical matter fields, distorted by higher derivative gravity, or infested with various forms of quantum hair. In many cases it is found that the entropy is simply related to the area of the event horizon: S = k A_H/(4\ell_P^2). For example, the ``entropy = (1/4) area'' law *holds* for: Schwarzschild, Reissner--Nordstrom, Kerr--Newman, and dilatonic black holes. On the other hand, the ``entropy = (1/4) area'' law *fails* for: various types of (Riemann)^n gravity, Lovelock gravity, and various versions of quantum hair. The pattern underlying these results is less than clear. This paper systematizes these results by deriving a general formula for the entropy: S = {k A_H/(4\ell_P^2)} + {1/T_H} \int_\Sigma [rho - {L}_E ] K^\mu d\Sigma_\mu + \int_\Sigma s V^\mu d\Sigma_\mu. (K^\mu is the timelike Killing vector, V^\mu the four velocity of a co--rotating observer.) If no hair is present the validity of the ``entropy = (1/4) area'' law reduces to the question of whether or not the Lorentzian energy density for the system under consideration is formally equal to the Euclideanized Lagrangian. ****** To appear in Physical Review D 15 July 1993 ****** [Stylistic changes, minor typos fixed, references updated, discussion of the Born-Infeld system excised]Comment: plain LaTeX, 17 pages, minor revision

Quantum Cosmology for a Quadratic Theory of Gravity

For pure fourth order (${\cal{L}} \propto R^2$) quantum cosmology the Wheeler-DeWitt equation is solved exactly for the closed homogeneous and isotropic model. It is shown that by imposing as boundary condition that $\Psi = 0$ at the origin of the universe the wave functions behave as suggested by Vilenkin.Comment: 13 pages, latex,no figure

Extended Gravity Theories and the Einstein-Hilbert Action

I discuss the relation between arbitrarily high-order theories of gravity and scalar-tensor gravity at the level of the field equations and the action. I show that $(2n+4)$-order gravity is dynamically equivalent to Brans-Dicke gravity with an interaction potential for the Brans-Dicke field and $n$ further scalar fields. This scalar-tensor action is then conformally equivalent to the Einstein-Hilbert action with $n+1$ scalar fields. This clarifies the nature and extent of the conformal equivalence between extended gravity theories and general relativity with many scalar fields.Comment: 12 pages, Plain Latex, SUSSEX-AST-93/7-

Evolution of the Bianchi I, the Bianchi III and the Kantowski-Sachs Universe: Isotropization and Inflation

We study the Einstein-Klein-Gordon equations for a convex positive potential in a Bianchi I, a Bianchi III and a Kantowski-Sachs universe. After analysing the inherent properties of the system of differential equations, the study of the asymptotic behaviors of the solutions and their stability is done for an exponential potential. The results are compared with those of Burd and Barrow. In contrast with their results, we show that for the BI case isotropy can be reached without inflation and we find new critical points which lead to new exact solutions. On the other hand we recover the result of Burd and Barrow that if inflation occurs then isotropy is always reached. The numerical integration is also done and all the asymptotical behaviors are confirmed.Comment: 22 pages, 12 figures, Self-consistent Latex2e File. To be published in Phys. Rev.

Exponential potentials and cosmological scaling solutions

We present a phase-plane analysis of cosmologies containing a barotropic fluid with equation of state $p_\gamma = (\gamma-1) \rho_\gamma$, plus a scalar field $\phi$ with an exponential potential $V \propto \exp(-\lambda \kappa \phi)$ where $\kappa^2 = 8\pi G$. In addition to the well-known inflationary solutions for $\lambda^2 3\gamma$ in which the scalar field energy density tracks that of the barotropic fluid (which for example might be radiation or dust). We show that the scaling solutions are the unique late-time attractors whenever they exist. The fluid-dominated solutions, where $V(\phi)/\rho_\gamma \to 0$ at late times, are always unstable (except for the cosmological constant case $\gamma = 0$). The relative energy density of the fluid and scalar field depends on the steepness of the exponential potential, which is constrained by nucleosynthesis to $\lambda^2 > 20$. We show that standard inflation models are unable to solve this `relic density' problem.Comment: 6 pages RevTeX file with four figures incorporated (uses RevTeX and epsf). Matches published versio

Black Holes with a Generalized Gravitational Action

Microscopic black holes are sensitive to higher dimension operators in the gravitational action. We compute the influence of these operators on the Schwarzschild solution using perturbation theory. All (time reversal invariant) operators of dimension six are included (dimension four operators don't alter the Schwarzschild solution). Corrections to the relation between the Hawking temperature and the black hole mass are found. The entropy is calculated using the Gibbons-Hawking prescription for the Euclidean path integral and using naive thermodynamic reasoning. These two methods agree, however, the entropy is not equal to 1/4 the area of the horizon.Comment: plain tex(uses phyzzx.tex), 8 pages, CALT-68-185

Quantum Cosmology and Higher-Order Lagrangian Theories

In this paper the quantum cosmological consequences of introducing a term cubic in the Ricci curvature scalar $R$ into the Einstein--Hilbert action are investigated. It is argued that this term represents a more generic perturbation to the action than the quadratic correction usually considered. A qualitative argument suggests that there exists a region of parameter space in which neither the tunneling nor the no-boundary boundary conditions predict an epoch of inflation that can solve the horizon and flatness problems of the big bang model. This is in contrast to the $R^2$--theory.Comment: 13 pages, LaTeX, preprint FERMILAB-Pub-94/XXX-A, March 199

Charged black holes in effective string theory

We investigate the qualitative new features of charged dilatonic black holes which emerge when both the Yang-Mills and Gauss-Bonnet curvature corrections are included in the effective action. We consider perturbative effects by an expansion up to second order in the inverse string tension on the four dimensional Schwarzschild background and determine the backreaction. We calculate the thermodynamical functions and show that for magnetic charge above a critical value, the temperature of the black hole has a maximum and goes to zero for a finite value of the mass. This indicates that the conventional Hawking evaporation law is modified by string theory at a classical level.Comment: 17 pages, 5 figures not included, plain Te