Quantization of Black Holes in the Wheeler-DeWitt Approach

We discuss black hole quantization in the Wheeler-DeWitt approach. Our consideration is based on a detailed investigation of the canonical formulation of gravity with special considerations of surface terms. Since the phase space of gravity for non-compact spacetimes or spacetimes with boundaries is ill-defined unless one takes boundary degrees of freedom into account, we give a Hamiltonian formulation of the Einstein-Hilbert-action as well as a Hamiltonian formulation of the surface terms. It then is shown how application to black hole spacetimes connects the boundary degrees of freedom with thermodynamical properties of black hole physics. Our treatment of the surface terms thereby naturally leads to the Nernst theorem. Moreover, it will produce insights into correlations between the Lorentzian and the Euclidean theory. Next we discuss quantization, which we perform in a standard manner. It is shown how the thermodynamical properties can be rediscovered from the quantum equations by a WKB like approximation scheme. Back reaction is treated by going beyond the first order approximation. We end our discussion by a rigorous investigation of the so-called BTZ solution in 2+1 dimensional gravity.Comment: 28 pages, 2 figure

COMPONENTS ASSOCIATED WITH PERCEIVED STUDENT SATISFACTION IN A TECHNOLOGY ENHANCED SECONDARY ASTRONOMY COURSE

A technology-enhanced course has many components that contribute to student satisfaction. Although technology plays a role in the delivery of instruction, the focus of this study was to identify student satisfaction with several Components: modes of discussion, modes of research, types of learning activities, modes of submitting assignments, modes of testing, and format of course materials. Additionally, the study described relationships between the learning styles and self-reported measures of student satisfaction for the 19 students in the study.Results from this study indicated that participants were more satisfied with chat room discussions, web-based research, web-based testing, and online availability of course materials and grades than with techniques used in traditional classrooms. Based upon these results, a teacher who is concerned about student satisfaction in technology-enhanced courses should be aware that these teaching techniques were more satisfying to students in a technology-enhanced astronomy course. It would be useful to do more study of the characteristics of technology-enhanced courses that affect student satisfaction and related outcomes

Ehrenfest's Principle and the Problem of Time in Quantum Gravity

We elaborate on a proposal made by Greensite and others to solve the problem of time in quantum gravity. The proposal states that a viable concept of time and a sensible inner product can be found from the demand for the Ehrenfest equations to hold in quantum gravity. We derive and discuss in detail exact consistency conditions from both Ehrenfest equations as well as from the semiclassical approximation. We also discuss consistency conditions arising from the full field theory. We find that only a very restricted class of solutions to the Wheeler-DeWitt equation fulfills all consistency conditions. We conclude that therefore this proposal must either be abandoned as a means to solve the problem of time or, alternatively, be used as an additional boundary condition to select physical solutions from the Wheeler-DeWitt equation.Comment: 20 pages, LATE

Dualities Compositeness and Spacetime Structure of 4d Extreme Stringy Black Holes

We study the BPS black hole solutions of the (truncated) action for heterotic string theory compactified on a six-torus. The O(3,Z) duality symmetry of the theory, together with the bound state interpretation of extreme black holes, is used to generate the whole spectrum of the solutions. The corresponding spacetime structures, written in terms of the string metric, are analyzed in detail. In particular, we show that only the elementary solutions present naked singularities. The bound states have either null singularities (electric solutions) or are regular (magnetic or dyonic solutions) with near-horizon geometries given by the product of two 2d spaces of constant curvature. The behavior of some of these solutions as supersymmetric attractors is discussed. We also show that our approach is very useful to understand some of the puzzling features of charged black hole solutions in string theory.Comment: 17 pages, LaTex, no figure

Cholinergic and GABAergic pathways in fly motion vision

BACKGROUND: The fly visual system is a highly ordered brain structure with well-established physiological and behavioral functions. A large number of interneurons in the posterior part of the third visual neuropil, the lobula plate tangential cells (LPTCs), respond to visual motion stimuli. In these cells the mechanism of motion detection has been studied in great detail. Nevertheless, the cellular computations leading to their directionally selective responses are not yet fully understood. Earlier studies addressed the neuropharmacological basis of the motion response in lobula plate interneurons. In the present study we investigated the distribution of the respective neurotransmitter receptors in the fly visual system, namely nicotinic acetylcholine receptors (nAChRs) and GABA receptors (GABARs) demonstrated by antibody labeling. RESULTS: The medulla shows a laminar distribution of both nAChRs and GABARs. Both receptor types are present in layers that participate in motion processing. The lobula also shows a characteristic layering of immunoreactivity for either receptor in its posterior portion. Furthermore, immunostaining for nAChRs and GABARs can be observed in close vicinity of lobula plate tangential cells. Immunostaining of GABAergic fibers suggests that inhibitory inputs from the medulla are relayed through the lobula to the lobula plate rather than through direct connections between medulla and lobula plate. CONCLUSIONS: The interaction of excitatory and inhibitory pathways is essential for the computation of visual motion responses and discussed in the context of the Reichardt model for motion detection

Semiclassical quantum states for black holes

I discuss the semiclassical approximation for the Wheeler-DeWitt equation when applied to the CGHS model and spherically symmetric gravity. Special attention is devoted to the issues of Hawking radiation, decoherence of semiclassical states, and black hole entropy.Comment: 8 pages, LATEX, contribution for the Second Conference on Constrained Dynamics and Quantum Gravity, Santa Margherita, Italy, September 199