Gravitational Collapse of a Radiating Shell

We study the collapse of a self-gravitating and radiating shell. Matter constituting the shell is quantized and the construction is viewed as a semiclassical model of possible black hole formation. It is shown that the shell internal degrees of freedom are excited by the quantum non-adiabaticity of the collapse and, consequently, on coupling them to a massless scalar field, the collapsing matter emits a burst of coherent (thermal) radiation.Comment: LaTeX, 34 pages, 21 EPS figures include

Black Holes in Magnetic Monopoles

We study magnetically charged classical solutions of a spontaneously broken gauge theory interacting with gravity. We show that nonsingular monopole solutions exist only if the Higgs vacuum expectation value $v$ is less than or equal to a critical value $v_{cr}$, which is of the order of the Planck mass. In the limiting case the monopole becomes a black hole, with the region outside the horizon described by the critical Reissner-Nordstrom solution. For $v<v_{cr}$, we find additional solutions which are singular at $r=0$, but which have this singularity hidden within a horizon. These have nontrivial matter fields outside the horizon, and may be interpreted as small black holes lying within a magnetic monopole. The nature of these solutions as a function of $v$ and of the total mass $M$ and their relation to the Reissner-Nordstrom solutions is discussed.Comment: (28 pages

Relational time in generally covariant quantum systems: four models

We analize the relational quantum evolution of generally covariant systems in terms of Rovelli's evolving constants of motion and the generalized Heisenberg picture. In order to have a well defined evolution, and a consistent quantum theory, evolving constants must be self-adjoint operators. We show that this condition imposes strong restrictions to the choices of the clock variables. We analize four cases. The first one is non- relativistic quantum mechanics in parametrized form. We show that, for the free particle case, the standard choice of time is the only one leading to self-adjoint evolving constants. Secondly, we study the relativistic case. We show that the resulting quantum theory is the free particle representation of the Klein Gordon equation in which the position is a perfectly well defined quantum observable. The admissible choices of clock variables are the ones leading to space-like simultaneity surfaces. In order to mimic the structure of General Relativity we study the SL(2R) model with two Hamiltonian constraints. The evolving constants depend in this case on three independent variables. We show that it is possible to find clock variables and inner products leading to a consistent quantum theory. Finally, we discuss the quantization of a constrained model having a compact constraint surface. All the models considered may be consistently quantized, although some of them do not admit any time choice such that the equal time surfaces are transversal to the orbits.Comment: 18 pages, revtex fil

Exact Dirac Quantization of All 2-D Dilaton Gravity Theories

The most general dilaton gravity theory in 2 spacetime dimensions is considered. A Hamiltonian analysis is performed and the reduced phase space, which is two dimensional, is explicitly constructed in a suitable parametrization of the fields. The theory is then quantized via the Dirac method in a functional Schrodinger representation. The quantum constraints are solved exactly to yield the (spatial) diffeomorphism invariant quantum wave functional for all theories considered. This wave function depends explicitly on the (single) configuration space coordinate as well as on the imbedding of space into spacetime (i.e. on the choice of time).Comment: 11 pages, LateX, (Equations (36) and (37) have been corrected and the discussion of them modified.

Validation testing of the EERC pilot-scale circulating fluidized-bed combustor using Salt Creek coal

The overall goal of the project was to provide a technical basis for assessing the economic and environmental feasibility of circulating fluidized-bed combustion (CFBC) technology, focusing on the effect of system configuration and coal properties on performance. Other underlying goals of the program were to (1) design and construct a CFBC test facility, thereby providing a test facility at an independent laboratory; (2) demonstrate that the test unit is capable of meeting the original design objectives; and (3) assess the ability of the unit to provide scalable data. The purpose of this interim report is to present data from validation testing to establish the scalability of data generated from this unit

On the Schroedinger Representation for a Scalar Field on Curved Spacetime

It is generally known that linear (free) field theories are one of the few QFT that are exactly soluble. In the Schroedinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the usual Fock representation is described by a Gaussian measure. In this paper, arbitrary globally hyperbolic space-times and embeddings of the Cauchy surface are considered. The classical structures relevant for quantization are used for constructing the Schroedinger representation in the general case. It is shown that in this case, the measure is also Gaussian. Possible implications for the program of canonical quantization of midisuperspace models are pointed out.Comment: 11 pages, Revtex, no figure

The Semi-Classical Back Reaction to Black Hole Evaporation

The semi-classical back reaction to black hole evaporation (wherein the renormalized energy momentum tensor is taken as source of Einstein's equations) is analyzed in detail. It is proven that the mass of a Schwarzshild black hole decreases according to Hawking's law $dM/dt = - C/ M^2$ where $C$ is a constant of order one and that the particles are emitted with a thermal spectrum at temperature $1/8\pi M(t)$.Comment: 10 pages, LATE

Adiabatic Invariant Treatment of a Collapsing Sphere of Quantized Dust

The semiclassical collapse of a sphere of quantized dust is studied. A Born-Oppenheimer decomposition is performed for the wave function of the system and the semiclassical limit is considered for the gravitational part. The method of adiabatic invariants for time dependent Hamiltonians is then employed to find (approximate) solutions to the quantum dust equations of motions. This allows us to obtain corrections to the adiabatic approximation of the dust states associated with the time evolution of the metric. The diverse non-adiabatic corrections are generally associated with particle (dust) creation and related fluctuations. The back-reaction due to the dominant contribution to particle creation is estimated and seen to slow-down the collapse.Comment: LaTeX, 16 pages, no figures, final version to appear in Class. and Quantum Gravit

EERC pilot-scale CFBC evaluation facility Project CFB test results

Project CFB was initiated at the University of North Dakota Energy and Environmental Research Center (EERC) in May 1988. Specific goals of the project were to (1) construct a circulating fluidized-bed combustor (CFBC) facility representative of the major boiler vendors' designs with the capability of producing scalable data, (2) develop a database for use in making future evaluations of CFBC technology, and (3) provide a facility for evaluating fuels, free of vendor bias for use in the - energy industry. Five coals were test-burned in the 1-MWth unit: North Dakota and Asian lignites, a Wyoming subbituminous, and Colorado and Pennsylvania bituminous coats. A total of 54 steady-state test periods were conducted, with the key test parameters being the average combustor temperature, excess air, superficial gas velocity, calcium-to-sulfur molar ratio, and the primary air-to-secondary air split. The capture for a coal fired in a CFBC is primarily dependent upon the total alkali-to-sulfur ratio. The required alkali-to ratio for 90% sulfur retention ranged from 1.4 to 4.9, depending upon coal type. While an alkali-to-ratio of 4.9 was required to meet 90% sulfur retention for the Salt Creek coal versus 1.4 for the Asian lignite, the total amount of sorbent addition required is much less for the Salt Creek coal, 4.2 pound sorbent per million Btu coal input, versus 62 pound/million Btu for the Asian lignite. The bituminous coals tested show optimal capture at combustor temperatures of approximately 1550[degree]F, with low-rank coals having optimal sulfur capture approximately 100[degree]F lower

Surface gravity in dynamical spherically symmetric spacetimes

A definition of surface gravity at the apparent horizon of dynamical spherically symmetric spacetimes is proposed. It is based on a unique foliation by ingoing null hypersurfaces. The function parametrizing the hypersurfaces can be interpreted as the phase of a light wave uniformly emitted by some far-away static observer. The definition gives back the accepted value of surface gravity in the static case by virtue of its nonlocal character. Although the definition is motivated by the behavior of outgoing null rays, it turns out that there is a simple connection between the generalized surface gravity, the acceleration of any radially moving observer, and the observed frequency change of the infalling light signal. In particular, this gives a practical and simple method of how any geodesic observer can determine surface gravity by measuring only the redshift of the infalling light wave. The surface gravity can be expressed as an integral of matter field quantities along an ingoing null line, which shows that it is a continuous function along the apparent horizon. A formula for the area change of the apparent horizon is presented, and the possibility of thermodynamical interpretation is discussed. Finally, concrete expressions of surface gravity are given for a number of four-dimensional and two-dimensional dynamical black hole solutions.Comment: 35 pages, revtex, 3 figures included using eps