Constraints in Quantum Geometrodynamics

We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3--geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the traditional dynamical equations obsolete. Quantization of the constraints in both the Dirac and ADM square root Hamiltonian approaches leads to the well known problems of time evolution. These problems of time are of both an interpretational and technical nature. In contrast, the geometrodynamic quantization procedure on the superspace of the true dynamical variables separates the issues of quantization from the enforcement of the constraints. The resulting theory takes into account states that are off-shell with respect to the constraints, and thus avoids the problems of time. We develop, for the first time, the geometrodynamic quantization formalism in a general setting and show that it retains all essential features previously illustrated in the context of homogeneous cosmologies.Comment: 36 pages, no figures, submitted to IJMPA, Rewording, Fixed Typo

A nonlinear quantum model of the Friedmann universe

A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This leads to a quantisation scheme that yields a Schrodinger-type equation which is in general nonlinear in evolution. Nevertheless it is compatible with a probabilistic interpretation of quantum mechanics and in particular the construction of a Hilbert space with a Euclidean norm is possible. The new scheme is applied to the quantisation of a Friedmann Universe with a massive scalar field whose dynamical behaviour is investigated numerically.Comment: 11 pages of text + 4 pages for 8 figure

Spin Dynamics of the LAGEOS Satellite in Support of a Measurement of the Earth's Gravitomagnetism

LAGEOS is an accurately-tracked, dense spherical satellite covered with 426 retroreflectors. The tracking accuracy is such as to yield a medium term (years to decades) inertial reference frame determined via relatively inexpensive observations. This frame is used as an adjunct to the more difficult and data intensive VLBI absolute frame measurements. There is a substantial secular precession of the satellite's line of nodes consistent with the classical, Newtonian precession due to the non-sphericity of the earth. Ciufolini has suggested the launch of an identical satellite (LAGEOS-3) into an orbit supplementary to that of LAGEOS-1: LAGEOS-3 would then experience an equal and opposite classical precession to that of LAGEOS-1. Besides providing a more accurate real-time measurement of the earth's length of day and polar wobble, this paired-satellite experiment would provide the first direct measurement of the general relativistic frame-dragging effect. Of the five dominant error sources in this experiment, the largest one involves surface forces on the satellite, and their consequent impact on the orbital nodal precession. The surface forces are a function of the spin dynamics of the satellite. Consequently, we undertake here a theoretical effort to model the spin ndynamics of LAGEOS. In this paper we present our preliminary results.Comment: 16 pages, RevTeX, LA-UR-94-1289. (Part I of II, postscript figures in Part II

Оценка динамики артросонографическихпоказателей при длительном лечениигонартроза Терафлексом( 3-летнее наблюдение)

Two hundred and forty-four outpatients with gonarthrosis were examined. The time course of arthrosonographic (the height of the articular cartilage, the volume of intraarticular effusion, the width of the joint cleft, and the degree of osteophytosis) changes were estimated during longterm Teraflex therapy and in control patients. The long-term (3-year) Teraflex therapy was shown to have a restraining impact on the processes of articular cartilage degradation and the progression of articular structural changes and to exert an anti-inflammatory effect.Обследовано 244 амбулаторных пациента с гонартрозом. Оценены в динамике артросонографические показатели (высота суставного хряща, объем выпота в полость сустава, ширина суставной щели, выраженность остеофитоза) на фоне длительного приема Терафлекса, а также в контроле. Показано сдерживающее влияние длительной терапии (на протяжении 3 лет) Терафлексом на процессы деградации суставного хряща, прогрессирование структурных изменений в суставах, продемонстрирован противовоспалительной эффект лечения препаратом

Numerical hydrodynamics in general relativity

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article the present update provides additional information on numerical schemes and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.Comment: 105 pages, 12 figures. The full online-readable version of this article, including several animations, will be published in Living Reviews in Relativity at http://www.livingreviews.or