On the Canonical Reduction of Spherically Symmetric Gravity

In a thorough paper Kuchar has examined the canonical reduction of the most general action functional describing the geometrodynamics of the maximally extended Schwarzschild geometry. This reduction yields the true degrees of freedom for (vacuum) spherically symmetric general relativity. The essential technical ingredient in Kuchar's analysis is a canonical transformation to a certain chart on the gravitational phase space which features the Schwarzschild mass parameter $M_{S}$, expressed in terms of what are essentially Arnowitt-Deser-Misner variables, as a canonical coordinate. In this paper we discuss the geometric interpretation of Kuchar's canonical transformation in terms of the theory of quasilocal energy-momentum in general relativity given by Brown and York. We find Kuchar's transformation to be a ``sphere-dependent boost to the rest frame," where the ``rest frame'' is defined by vanishing quasilocal momentum. Furthermore, our formalism is general enough to cover the case of (vacuum) two-dimensional dilaton gravity. Therefore, besides reviewing Kucha\v{r}'s original work for Schwarzschild black holes from the framework of hyperbolic geometry, we present new results concerning the canonical reduction of Witten-black-hole geometrodynamics.Comment: Revtex, 35 pages, no figure

New variables, the gravitational action, and boosted quasilocal stress-energy-momentum

This paper presents a complete set of quasilocal densities which describe the stress-energy-momentum content of the gravitational field and which are built with Ashtekar variables. The densities are defined on a two-surface $B$ which bounds a generic spacelike hypersurface $\Sigma$ of spacetime. The method used to derive the set of quasilocal densities is a Hamilton-Jacobi analysis of a suitable covariant action principle for the Ashtekar variables. As such, the theory presented here is an Ashtekar-variable reformulation of the metric theory of quasilocal stress-energy-momentum originally due to Brown and York. This work also investigates how the quasilocal densities behave under generalized boosts, i. e. switches of the $\Sigma$ slice spanning $B$. It is shown that under such boosts the densities behave in a manner which is similar to the simple boost law for energy-momentum four-vectors in special relativity. The developed formalism is used to obtain a collection of two-surface or boost invariants. With these invariants, one may ``build" several different mass definitions in general relativity, such as the Hawking expression. Also discussed in detail in this paper is the canonical action principle as applied to bounded spacetime regions with ``sharp corners."Comment: Revtex, 41 Pages, 4 figures added. Final version has been revised and improved quite a bit. To appear in Classical and Quantum Gravit

Hamiltonians for a general dilaton gravity theory on a spacetime with a non-orthogonal, timelike or spacelike outer boundary

A generalization of two recently proposed general relativity Hamiltonians, to the case of a general (d+1)-dimensional dilaton gravity theory in a manifold with a timelike or spacelike outer boundary, is presented.Comment: 17 pages, 3 figures. Typos correcte

Influence of Stokes number on the velocity and concentration distributions in particle-laden jets

The first measurement of the influence of the Stokes number on the distributions of particle concentration and velocity at the exit of a long pipe are reported, together with the subsequent influence on the downstream evolution of these distributions through a particle-laden jet in co-flow. The data were obtained by simultaneous particle image velocimetry (PIV) and planar nephelometry (PN), using four cameras to provide high resolution through the first 30 jet diameters and also correction for optical attenuation. These data provide much more detailed information than is available from previous measurements. From them, a new understanding is obtained of how the Stokes number influences the flow at the jet exit plane and how this influence propagates throughout the jet.Timothy C. W. Lau and Graham J. Natha

The effect of Stokes number on particle velocity and concentration distributions in a well-characterised, turbulent, co-flowing two-phase jet

Published online: 09 November 2016Simultaneous measurements of particle velocity and concentration (number density) in a series of mono-disperse, two-phase turbulent jets issuing from a long, round pipe into a low velocity co-flow were performed using planar nephelometry and digital particle image velocimetry. The exit Stokes number, SkD, was systematically varied over two orders of magnitude between 0.3 and 22.4, while the Reynolds number was maintained in the turbulent regime (10000⩽ReD⩽40000). The mass loading was fixed at ϕ=0.4, resulting in a flow that is in the two-way coupling regime. The results show that, in contrast to all previous work where a single Stokes number has been used to characterise fluid–particle interactions, the characteristic Stokes number in the axial direction is lower than that for the radial direction. This is attributed to the significantly greater length scales in the axial motions than in the radial ones. It further leads to a preferential response of particles to gas-phase axial velocity fluctuations, u′p, over radial velocity fluctuations, v′p. This, in turn, leads to high levels of anisotropy in the particle-phase velocity fluctuations, u′p/v′p>1, throughout the jet, with u′p/v′p increasing as SkD is increased. The results also show that the region within the first few diameters of the exit plane is characterised by a process of particle reorganisation, resulting in significant particle migration to the jet axis for SkD⩽2.8 and away from the axis for SkD⩾5.6. This migration, together with particle deceleration along the axis, causes local humps in the centreline concentration whose value can even exceed those at the exit plane.Timothy C. W. Lau and Graham J. Natha

A millimeter-wave antireflection coating for cryogenic silicon lenses

We have developed and tested an antireflection (AR) coating method for silicon lenses at cryogenic temperatures and millimeter wavelengths. Our particular application is a measurement of the cosmic microwave background. The coating consists of machined pieces of Cirlex glued to the silicon. The measured reflection from an AR coated flat piece is less than 1.5% at the design wavelength. The coating has been applied to flats and lenses and has survived multiple thermal cycles from 300 to 4 K. We present the manufacturing method, the material properties, the tests performed, and estimates of the loss that can be achieved in practical lenses