Is nonrelativistic gravity possible?

We study nonrelativistic gravity using the Hamiltonian formalism. For the dynamics of general relativity (relativistic gravity) the formalism is well known and called the Arnowitt-Deser-Misner (ADM) formalism. We show that if the lapse function is constrained correctly, then nonrelativistic gravity is described by a consistent Hamiltonian system. Surprisingly, nonrelativistic gravity can have solutions identical to relativistic gravity ones. In particular, (anti-)de Sitter black holes of Einstein gravity and IR limit of Horava gravity are locally identical.Comment: 4 pages, v2, typos corrected, published in Physical Review

Quasi-static vapor pressure measurements on reactive systems in inert atmosphere box

Apparatus makes vapor pressure measurements on air-sensitive systems in an inert atmosphere glove box. Once the apparatus is loaded with the sample and all connections made, all measuring operations may be performed outside the box. The apparatus is a single-tube adaptation of the double-tube quasi-static technique

An Introduction to Conformal Ricci Flow

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equations are analogous to the incompressible Navier-Stokes equations of fluid mechanics inasmuch as a conformal pressure arises as a Lagrange multiplier to conformally deform the metric flow so as to maintain the scalar curvature constraint. The equilibrium points are Einstein metrics with a negative Einstein constant and the conformal pressue is shown to be zero at an equilibrium point and strictly positive otherwise. The geometry of the conformal Ricci flow is discussed as well as the remarkable analytic fact that the constraint force does not lose derivatives and thus analytically the conformal Ricci equation is a bounded perturbation of the classical unnormalized Ricci equation. That the constraint force does not lose derivatives is exactly analogous to the fact that the real physical pressure force that occurs in the Navier-Stokes equations is a bounded function of the velocity. Using a nonlinear Trotter product formula, existence and uniqueness of solutions to the conformal Ricci flow equations is proven. Lastly, we discuss potential applications to Perelman's proposed implementation of Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur

Interaction Between Gravity Compensation Suspension System and Deployable Structure

Gravity compensation suspension systems are essential to support space structures during tests on Earth, but also impose constraints on the structures that have the effect of changing their behavior. A computational and experimental study of the interaction of a rigid panel solar array model with a manually adjustable suspension system during quasi-static deployment tests in the 1-g environment of the laboratory is presented. A methodology is established for modeling this interaction, for predicting the effects of suspension system adjustments, and for optimization of the suspension system through these adjustments. Some improvements can be achieved by manual adjustments, but further optimization requires an active system

Measurement of the Mass Profile of Abell 1689

In this letter we present calibrated mass and light profiles of the rich cluster of galaxies Abell 1689 out to 1 $h^{-1}$ Mpc from the center. The high surface density of faint blue galaxies at high redshift, selected by their low surface brightness, are unique tools for mapping the projected mass distribution of foreground mass concentrations. The systematic gravitational lens distortions of $10^4$ of these background galaxies in 15\arcmin\ fields reveal detailed mass profiles for intervening clusters of galaxies, and are a direct measure of the growth of mass inhomogeneity. The mass is measured directly, avoiding uncertainties encountered in velocity or X-ray derived mass estimates. Mass in the rich cluster Abell 1689 follows smoothed light, outside 100 h$^{-1}$ kpc, with a rest-frame V band mass-to-light ratio of $400 \pm 60$ $h^{-1} (M/L_V)_\odot$. Near the cluster center, mass appears to be more smoothly distributed than light. Out to a radius of 1 $h^{-1}$ Mpc the total mass follows a steeper than isothermal profile. Comparing with preliminary high resolution N-body clustering simulations for various cosmogonies on these scales, these data are incompatible with hot dark matter, a poor fit to most mixed dark matter models, and favor open or $\Lambda > 0$ cold dark matter. Substructure is seen in both the mass and the light, but detailed correspondence is erased on scales less than 100 $h^{-1}$ kpc.Comment: 13 pages, uuencoded, compressed postscript file, 2 figures included additional 1Mbyte figure available on request. Only change is that in original errorbars on Fig. 5 were a factor of 2 too big

Topics in the Dynamics or General Relativity

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The Einstein Equations of Evolution - A Geometric Approach

In this paper the exterior Einstein equations are explored from a differential geometric point of view. Using methods of global analysis and infinite-dimensional geometry, we answer sharply the question: "In what sense are the Einstein equations, written as equations of evolution, a Lagrangian dynamical system?" By using our global methods, several aspects of the lapse function and shift vector field are clarified. The geometrical significance of the shift becomes apparent when the Einstein evolution equations are written using Lie derivatives. The evolution equations are then interpreted as evolution equations as seen by an observer in space coordinates. Using the notion of body-space transitions, we then find the relationship between solutions with different shifts by finding the flow of a time-dependent vector field. The use of body and space coordinates is shown to be somewhat analogous to the use of such coordinates in Euler's equations for a rigid body and the use of Eulerian and Lagrangian coordinates in hydrodynamics. We also explore the geometry of the lapse function, and show how one can pass from one lapse function to another by integrating ordinary differential equations. This involves integrating what we call the "intrinsic shift vector field." The essence of our method is to extend the usual configuration space [fraktur M]=Riem(M) of Riemannian metrics to [script T]×[script D]×[fraktur M], where [script T]=C[infinity](M,R) is the group of relativistic time translations and [script D]=Diff(M) is the group of spatial coordinate transformations of M. The lapse and shift then enter the dynamical picture naturally as the velocities canonically conjugate to the configuration fields (xit,etat)[is-an-element-of][script T]×[script D]. On this extended configuration space, a degenerate Lagrangian system is constructed which allows precisely for the arbitrary specification of the lapse and shift functions. We reinterpret a metric given by DeWitt for [fraktur M] as a degenerate metric on [script D]×[fraktur M]. On [script D]×[fraktur M], however, the metric is quadratic in the velocity variables. The groups [script T] and [script D] also serve as symmetry groups for our dynamical system. We establish that the associated conserved quantities are just the usual "constraint equations." A precise theorem is given for a remark of Misner that in an empty space-time we must have [script H]=0. We study the relationship between the evolution equations for the time-dependent metric gt and the Ricci flat condition of the reconstructed Lorentz metric gL. Finally, we make some remarks about a possible "superphase space" for general relativity and how our treatment on [script T]×[script D]×[fraktur M] is related to ordinary superspace and superphase space

Efficient SAR Raw Data Compression in Frequency Domain

SAR raw data compression is necessary to reduce huge amounts of SAR data for a memory on board a satellite, space shuttle or aircraft and for later downlink to a ground station. In view of interferometric and polarimetric applications for SAR data, it becomes more and more important to pay attention to phase errors caused by data compression. Herein, a detailed comparison of block adaptive quantization in time domain (BAQ) and in frequency domain (FFT-BAQ) is given. Inclusion of raw data compression in the processing chain allows an efficient use of the FFT-BAQ and makes implementation for on-board data compression feasible. The FFT-BAQ outperforms the BAQ in terms of signal-to-quantization noise ratio and phase error and allows a direct decimation of the oversampled data equivalent to FIR-filtering in time domain. Impacts on interferometric phase and coherency are also given

Studying pion effects on the chiral phase transition

We investigate the chiral phase transition at finite temperatures and zero chemical potential with Dyson-Schwinger equations. Our truncation for the quark-gluon interaction includes mesonic degrees of freedom, which allows us to study the impact of the pions on the nature of the phase transition. Within the present scheme we find a five percent change of the critical temperature due to the pion backreaction whereas the mean field character of the transition is not changed.Comment: 2 pages, 2 figures, talk given by J.A.M. at the 30th International School of Nuclear Physics, Erice, Sicily from 16 - 24 September 200